NQF Level: 2 US No: 9009

Learner Guide
Primary Agriculture

The us e of s ta ti s ti cs
& pr o b a b i l i t y t o
i nv e s t i g a t e l i f e
r e l a t e d pr o b l e m s

My name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Company: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Commodity: . . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . .

The availability of this product is due to the financial support of the National
Department of Agriculture and the AgriSETA. Terms and conditions apply.
 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
2

Before we start…
Dear Learner - This Learner Guide contains all the information to acquire all the
knowledge and skills leading to the unit standard:

Apply basic knowledge of statistics and probability to influence the use of data and
Title:
procedures in order to investigate life related problems
US No: 9009 NQF Level: 2 Credits: 3

The full unit standard will be handed to you by your facilitator. Please read the unit
standard at your own time. Whilst reading the unit standard, make a note of your
questions and aspects that you do not understand, and discuss it with your
facilitator.

This unit standard is one of the building blocks in the qualifications listed below.
Please mark the qualification you are currently doing:

Title ID Number NQF Level Credits Mark

National Certificate in Animal Production 48976 2 120
National Certificate in Mixed Farming Systems 48977 2 120
National Certificate in Plant Production 48975 2 120

Are you enrolled in a: Y N

Please mark the learning program you
Learnership?
are enrolled in:
Skills Program?
Your facilitator should explain the above
Short Course?
concepts to you.

You will also be handed a Learner Workbook. This Learner Workbook should be used
in conjunction with this Learner Guide. This Learner Guide contains all the
information, and more, as well as the activities that you will be expected to do
during the course of your study. Please keep the activities that you have completed
and include it in your Portfolio of Evidence. Your PoE will be required during your
final assessment.

What is assessment all about?

You will be assessed during the course of your study. This is called formative
assessment. You will also be assessed on completion of this unit standard. This is
called summative assessment. Before your assessment, your assessor will discuss
the unit standard with you.

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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Assessment takes place at different intervals of the learning process and includes
various activities. Some activities will be done before the commencement of the
program whilst others will be done during programme delivery and other after
completion of the program.

The assessment experience should be user friendly, transparent and fair. Should
you feel that you have been treated unfairly, you have the right to appeal. Please
ask your facilitator about the appeals process and make your own notes.

How to use the activity sheets…

Your activities must be handed in from time to time on request of the facilitator for
the following purposes:

The activities that follow are designed to help you gain the skills, knowledge
and attitudes that you need in order to become competent in this learning
module.

It is important that you complete all the activities and worksheets, as directed
in the learner guide and at the time indicated by the facilitator.

It is important that you ask questions and participate as much as possible in

order to play an active roll in reaching competence.

When you have completed all the activities and worksheets, hand this
workbook in to the assessor who will mark it and guide you in areas where
additional learning might be required.

You should not move on to the next step in the assessment process until this
step is completed, marked and you have received feedback from the
assessor.

Sources of information to complete these activities should be identified by your

facilitator.

Please note that all completed activities, tasks and other items on which you
were assessed must be kept in good order as it becomes part of your
Portfolio of Evidence for final assessment.

Enjoy this learning experience!

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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
4

How to use this guide …

Throughout this guide, you will come across certain re-occurring “boxes”. These
boxes each represent a certain aspect of the learning process, containing
information, which would help you with the identification and understanding of these
aspects. The following is a list of these boxes and what they represent:

What does it mean? Each learning field is characterized by unique terms and
definitions – it is important to know and use these terms and definitions correctly. These
terms and definitions are highlighted throughout the guide in this manner.

You will be requested to complete activities, which could be group activities, or individual
activities. Please remember to complete the activities, as the facilitator will assess it and
these will become part of your portfolio of evidence. Activities, whether group or individual
activities, will be described in this box.

Examples of certain The following box indicates a summary of

concepts or principles to concepts that we have covered, and offers
help you contextualise you an opportunity to ask questions to your
them easier, will be shown facilitator if you are still feeling unsure of
in this box. the concepts listed.

My Notes …
You can use this box to jot down questions you might have, words that you do not understand,
instructions given by the facilitator or explanations given by the facilitator or any other remarks that
will help you to understand the work better.
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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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What are we going to learn?

What will I be able to do? .....................................................……………………… 6

Learning outcomes …………………………………………………………………………… 6

What do I need to know? .................................................…..……………………… 6

Session 1 Techniques to organise and represent data……………………… 7

Session 2 Implications resulting from modeled data...…………………….. 30

Am I ready for my test? ........................................................... 45

Checklist for Practical assessment.......................................... 47

Paperwork to be done.............................................................. 48

Bibliography............................................................................. 49

Terms and Conditions .............................................................. 49

Acknowledgements.................................................................. 50

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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What will I be able to do?

When you have achieved this unit standard, you will be able to:
Apply various techniques to organise and represent data in order to model
situations for specific purposes.
Give opinions on the implications of the modeled data for the required purpose.

Learning Outcomes
At the end of this learning module, you must is able to demonstrate a
basic knowledge and understanding of:
Methods for selecting, organizing data and calculating statistics
The meaning of concepts such as centre and spread
Techniques for representing and drawing conclusions from statistics.

What do I need to know?

It is expected of the learner attempting this unit standard to demonstrate
competence against the unit standard:
Mathematics and Communications at NQF level 1.

My Notes …
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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Session 1 T e c h n i q u e s t o or ga n i z e a n d
r e pr e s e n t da t a
After completing this session, you should be able to:
SO 1: Apply various techniques to organise and represent data in
order to model situations.

In this session we explore the following concepts:

select and use data from tables

record and organise data

calculate statistical data

use scales to represent statistical data

represent data

1.1 Data table

We often have to gather information to establish the trends and reality of situations.
Data tables assist us to organize this information logically so that it can be applied to
the purpose it was intended for. Data tables are similar to a register or record of
events or items that give us information and the information is given to use in rows
and columns. A row is any horizontal collection of data while a column is any vertical
collection of data.

Number of
African Coloured Asian White
students
Male 56 45 78 12 Row
Female 68 52 62 14
124 97 140 26
Total

Column

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Interpretation of Data.
The interpretation of data is very simple if you are able to work through it
systematically. The most important features of data are:

• frequency
• average
• modus
• median
• range
Frequency

Frequency is the number of times a certain value appears in a series of data.

Example: In the series of data below, the number 5 appears 6 times,
therefore the frequency of 5 is 6. It is the value that appears most often in
the series:

3; 5; 3; 7; 5; 6; 5; 9; 5; 2; 4; 4; 5; 5; 8
If we put this series of data in a table, then the frequency would be much
clearer:
Number Tally Frequency
0 0
1 0
2 І 1
3 ІІ 2
4 ІІ 2
5 ІІІІ І 6
6 І 1
7 І 1
8 І 1
9 І 1
10 0
15

Note: When you are using the tally system to determine the frequency, you
will draw a line for every time something occurs, i.e. І. When it occurs four
times, you draw four lines, i.e. І І І І, but when you reach the fifth occurrence,
you do not draw the fifth line next to the other four, but you draw a line
through the other our lines to show that you have reached 5, i.e. І І І І. It
makes it much easier to count when you reach the end.

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
9

Average

Adding together all the values and then dividing it by the number of items
calculate the average of a set of data. The average is also known as the
mean.
Example:
We will use our previous set of data:
3; 5; 3; 7; 5; 6; 5; 9; 5; 2; 4; 4; 5; 5; 8
To calculate the average, we first add together all the values:
3 + 5 + 3 + 7 + 5 + 6 + 5 + 9 + 5 + 2 + 4 + 4 + 5 + 5 + 8 = 126
Then we count how many items are there, i.e. 15

3, 5; 3; 7, 5; 6; 5; 9; 5; 2, 4, 4, 5, 5, 8 126

Number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
of Items

Average = (Sum of all the values) ÷ (number of items)

= 126 ÷ 15
= 8,4

Mode

The mode is the number that occurs most frequently in the series of data. In
the series of data below, the mode is 5.

3; 5; 3; 7; 5; 6; 5; 9; 5; 2; 4; 4; 5; 5; 8

Median

The median in a series of data is the number that is exactly in the middle, or
halfway between two numbers in the middle.

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
10

Example:

From our set of data:

3; 5; 3; 7; 5; 6; 5; 9; 5; 2; 4; 4; 5; 5; 8

We re-arrange it in chronological (numerical) order:

2; 3; 3; 4; 4; 5; 5; 5; 5; 5; 5; 6; 7; 8; 9

The median in this set of data is 5.

Range

The range is the difference between the highest number and the lowest
number in a set of data.

The range in the set of data we have been using as an example will be as
follows:

lowest number 2; 3; 3; 4; 4; 5; 5; 5; 5; 5; 5; 6; 7; 8; 9 highest number

Range = Highest Number – Lowest Number

=9–2

=7

Frequency table
A frequency table is the diagram that shows the number of times a particular
incident took place.
Example:

In a learnership class, the following scores were achieved for an assessment of a

learning programme by the 15 learners in the class:

56% 29% 65% 74% 42%

38% 92% 43% 98% 23%

64% 81% 66% 68% 69%

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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The facilitator wants to find answers to the following questions:

Which percentage appears most frequently?

Which percentage appears least frequently?

How many learners scored more than 80%?

How many learners scored less than 50%?

The first step would be to set up a frequency table:

Percentage Tally Frequency
0-10 0
11-20 0
21-30 ΙΙ 2
31-40 Ι 1
41-50 ΙΙ 2
51-60 Ι 1
61-70 ΙΙΙΙ 5
71-80 Ι 1
81-90 Ι 1
91-100 ΙΙ 2

15

Now we have a better idea of what the answers to the questions may be:
1. Which percentage appears most frequently? Between 61% and 70%
2. Which percentage appears least frequently? Between 0% and 20%
3
3. How many learners scored more than 80%? /15
5
4. How many learners scored less than 50%? /15

This information can now be used by the facilitator for various purposes, i.e.

• A third of the class got less than 50%. Do these learners need more
support?
• The average learner can be expected to score between 61% and 70% for
this learning assessment.

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
12

Stem-and-Leaf table
A stem-and-leaf method is similar to tally counting. Instead of using tallies, the
given data is divided (by a vertical line) into stems on the left and leaves on the
right.

Example:

24 Learners obtained the following marks out of 50 for a test.

49 38 31 27 20 48 37 31

23 41 33 10 15 34 22 35

21 39 31 27 20 19 35 26

The first digit forms the stem and the second digit the leaf.

The stem-and-leaf table will look like this:

1 0; 5; 9; 3
2 0; 0; 1; 2; 3; 6; 7; 7; 8
3 1; 1; 1; 3; 4; 5; 5; 7; 8; 9; 10
4 1; 8; 9; 3
24

Stem Leaf Check the total:

3 + 8 + 10 + 3 = 24

All data is shown on the table even if it appears many times.

From this stem-and-leaf table, we can conclude the following information:

• the frequency of learners who got 31marks is 3
• the average mark of the learners lies between 30 and 35
• the range is: 49 – 10 = 39

Please complete Activity My Notes …

1 at the end of the .....................................
session ......................................
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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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1.2 Graphs
Graphs are visual representations of what is written in a data table. There are many
types of graphs that we can use and it usually depends on what you need to
represent and to whom the representation is made.

Example

Bar graph Histogram

70

70
60
60
50
50
40
40

30
30

20 20

10 10

0 0
1
Plant 1 Plant 2 Plant 3 Plant 4

Broken Line Graphs

Pie Chart

70

60

50

40

30

20

10

0
Plant 1 Plant 2 Plant 3 Plant 4

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Pictograms
Pictograms are graphs that show us data by using identical pictures instead of
figures and lines.

Example

Susie has counted how many telephone calls the people in her department make
during the day. This is the data she has collected:
08:00 – 10:00 – 14:00 –
Name 12:00 – 14:00 Total
10:00 12:00 16:00
Janie 15 16 17 15 63
Henry 13 14 1 16 77
Thea 12 11 12 12 47
Malvin 13 10 13 13 49
Thys 11 12 11 10 44

She decides to draw up a pictogram to show the data she has collected. First she
rounds off the number of phone calls to the nearest ten:
Name Total Rounded off

Janie 63 60

Henry 77 80

Thea 47 50

Malvin 49 50

Thys 44 40

And then she uses a scale.

§ = 10 Telephone calls
Finally she draws up a pictogram to show the number of calls made by each person.
Name Total Telephone Calls for the Day

Janie §§§§§§
Henry §§§§§§§§
Thea §§§§§
Malvin §§§§§
Thys §§§§
The pictogram shows the number of telephone calls made in a visual and graphic
way.

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Bar Graphs and Histograms

A bar graph and a histogram can be used when the data needs to be grouped into
periods and the frequency of each period needs to be clarified.

The difference between the bar graph and the histogram is that when we draw a
histogram, we do not leave spaces between the columns as with the bar graph.
(Learning tip: the words bar graph have a space. Bar graphs have spaces. The word
histogram has no space, the actual graph has no spaces.)
Bar graphs are used when the data classes are not continuous e.g. in comparing
the annual yield of carrots, tomatoes and potatoes of a vegetable farm. There is no
intermediate between carrots and tomatoes. The classes are different from each
other.

Example of a bar graph:

A farmer wants to compare the amount of fuel used by a number of vehicles on his
farm. He has summarized the data in a table.

Vehicle Tractor Truck Bakkie Car

Litres of fuel used 730 100 545 150
in June 2006

He must construct a bar graph, because a truck is very different to a car.

Litres of fuel used by vehicles in June 2006

800
600
litres of fuel

400
200
0
tractor truck bakkie car
vehicle

Histograms are used if the data classes are continuous. For example, a farmer
wants to see how many tons of carrots a certain field produced per year from 2000
to 2006. There are no spaces between the bas, because 2000 borders on 2001.
Time is continuous. He could also use a line graph.

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Example of a histogram:

The same farmer wants to compare the amount of fuel used by his tractor each
month from January to June.

Month Jan Feb March Apr May June

Litres of fuel used by
550 456 458 624 576 730
tractor

He must draw a histogram because time is continuous.

Litres of fuel used by tractor in 2006

800 Jan
Litres of fuel

600 Feb
March
400
April
200 May
0 June
month

Example of a histogram with frequency classes

The owner of SUPERVEG has collected the following statistic with regards to the age
of the workers.

24 56 45 32 45 65 21 34 23 26

38 26 39 40 51 36 25 39 27 52

43 61 55 63 25 26 34 26 25 36

39 44 36 45 54 38 31 29 22 34

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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He puts this into a frequency table

Age Tally Frequency

0-20 0
21-30 1111 1111 111 13
31-40 1111 1111 1111 14
41-50 1111 5
51-60 1111 5
61-70 111 3
40

He then draws a histogram using the information he has gathered.

Ages of workers at SUPERVEG

15
21 - 30
frequency

10 31 - 40
41 - 50
5 51 - 60
61 - 70
0

Age classes

Pie Graphs

Pie graphs are graphs that represent the data as segments of a circle. The various
data will take up a certain angle of the total angles in a circle (360º).

Example

In a community, a researcher named Janet is collecting information about how many

people have access to telephones. She goes about asking questions to the
community and arrives home with the following data:

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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Frequency Table

Details Tally Frequency

Home 33
IIII IIII IIII IIII IIII IIII III
Telephone

Cellphone IIII IIII IIII IIII IIII IIII IIII IIII II 42

Public
IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII 50
Phone

No Access IIII IIII IIII IIII III 23

148

Janet now calculates the percentage and the segment of 360º that she will use to
draw up the pie graph:

Calculation table

Description Percentage of Total Degrees of 360º

33 33
/148 x 100 /148 x 360º
Home Telephone
≈ 22,3% ≈ 80º
42 42
/148 x 100 /148 x 360º
Cellphone
≈ 28,4% ≈ 102º
50 50
/148 x 100 /148 x 360º
Public Phone
≈ 33,8% ≈ 122º
23 23
/148 x 100 /148 x 360º
No Access
≈ 15,5% ≈ 56º

She checks her calculations:

Percentage 22,3 + 28,4 + 33,8 + 15,5 = 100

Degrees 80 + 102 + 122 + 56 = 360

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Now she can draw her Pie Graph:

Telephone Access

Home
22%
Public
34%

Cell
None 28%
16%

If you measure the angles of the different segments, you will find that they are
exactly as worked out in the calculation table.

Broken Line Graphs

When we were drawing the bar graph and histogram, we used the whole column to
show our data. With a broken line graph, we will only use points, not full columns.

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Example

At WITWAT Manufacturing, the production manager has collected data with regards
to the temperature at which a certain machine runs over a 12 hour period.
Broken Line Graph of Machine Temperature

108
107
106
105
104
103
102
101
100
99
98
97
96
95
94
93
92
91
90
06:00

07:00

08:00

09:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

18:00

If the production manager wants to see what the temperature on the machine was
at different times, then he can read it from the graph, i.e.:
• At 09:00 the temperature of the machine was 102º
• At 11:30 the temperature of the machine was 105º
• At 17:30 the temperature of the machine was 100º
He can also read the following information from the graph:
• at what time the machine is running at the highest temperature
• at what time the machine is running at the lowest temperature
• at what time the machine if running at 100º, etc.

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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
21

1.3 Probability
Probability is the possibility or chance that something might occur.

We work out probability by dividing the number of successful outcomes by the total
number of possible outcomes.

Example

Every Saturday night we watch the lotto and the winner of the game show gets to
draw a ball from a variety of balls in a round canister. We want to work out what
the probability is of the winner drawing the red ball, which will make him the winner
of a car.

First we have to find out how many balls are in the canister:

5 green balls
6 yellow balls

1 red ball (the winning ball)

There are 5 + 6 + 1 = 12 balls in the canister

number of successful outcomes

Probability (P) =
total number of possible outcomes

5
Probability (Green ball) = /12

6
Probability (Yellow ball) = /12

1
Probability (Red ball) = /12

So the chance of the winner drawing a red ball is 1 out of 12.

Please complete Activity My Notes …

2 at the end of the ....................................
session ....................................
....................................
....................................
....................................

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 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
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1
Individual Activity: My Name:
Answer the questions .......................
below My Workplace:
......................
SO 1 My ID Number:

1. The weather Bureau collected data from 25 weather stations in the Free State area
concerning the number of hours of bright sunshine during January and June 2005.

Hours of bright sunshine Hours of bright sunshine

January 2005 June 2005
211 221 193 182 210 227 152 142 132 164 152 105
214 207 205 206 194 207 115 105 121 126 171 121
217 171 225 181 189 192 117 136 104 121 126 126
209 209 175 169 189 203 119 142 135 148 139 147
206 131

a) Draw up a frequency table (tally format) for both January and June. Use the class
intervals 100 – 109, 110-119 etc

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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b) What is the modal class for January? …………………………………………………………

c) What is the modal class for June? ……………………………………………………………..

d) What can you conclude if you compare the two modal classes calculated

above? ……………………………………………………………………………………………………

e) Calculate the mean for both January and June.

f) Calculate the range for both January and June.

g) What conclusion can you reach if you compare the ranges calculated in f)? Is
your conclusion the same as the conclusion that you reached in d)?
……………………………………………………………………………………………………………………

………………………………………………………………………………………………………………….

……………………………………………………………………………………………………………………

………………………………………………………………………………………………………………...

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24

2. A farmer kept count of the number of litres of milk his cows produced per day.

35, 47, 34, 46, 62, 41, 35, 47, 51, 56, 73, 38, 41, 44, 51, 45, 74

a) Determine suitable class intervals. ……………………………………………………

b) Construct a stem-and-leaf diagram to show the data.

c) Determine the modal class of your distribution…………………………………..

d) On how many days were less than 40l of milk produced? …………………..
e) Rewrite the numbers in ascending (from smallest to biggest) and
determine the median value.
………………………………………………………………………………………………………………
……………………………………………………………………………………………………………..
………………………………………………………………………………………………………………
f) Give a reasonable explanation why the amount of milk produced varied
so much from day to day.
………………………………………………………………………………………………………………
……………………………………………………………………………………………………………..
………………………………………………………………………………………………………………

Facilitator comments: Assessment:

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
25

2
Individual Activity: My Name:
Answer the questions .......................
below My Workplace:
......................
SO 1 My ID Number:

1. In a Mathematics examination 40 learners scored the following marks in

percentages (%):

61 43 92 78 94 66 63 59 29 82
39 68 89 95 96 45 48 49 35 54
69 84 83 85 74 73 83 59 74 72
85 36 25 63 63 83 40 54 67 84

a) Draw up and complete a frequency table.

b) How many learners obtained more than 80%?

………………………………………………………………………………………………………
c) 60% is the accepted competency pass mark. How many learners are not
yet competent?
……………………………………………………………………………………………………….

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d) Show the data on a stem-and-leaf table. Answer the following questions:

• What is the median of the group?

………………………………………………………………………………………………………….
• What is the mode of the group?
………………………………………………………………………………………………………….
• What is the group average for mathematics?
………………………………………………………………………………………………………….
e) Draw a histogram using the frequency table.

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2. In an election there were three candidates: A, B and C. The number of votes

cast for each candidate is represented in the pie chart below. Candidate A got
1170 votes.

a. How many votes did candidate B get?

b. How many people voted altogether?

120º

B C

c. What percentage of the votes went to

candidate C?

3. There are 52 playing cards in a pack of cards. What is the probability that the
first card to be drawn is ...........

a. a queen
………………………………………………………………………………………………………..
b. an Ace
………………………………………………………………………………………………………..
c. a heart
………………………………………………………………………………………………………..
d. the king of clubs
………………………………………………………………………………………………………..

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4. A tour operator is given the following temperatures, in degrees Celsius, of the

following places in South Africa, in the middle of winter:
Johannesburg = 14
Durban = 24
Port Elizabeth = 20
Bloemfontein = 14
Springbok = 15
Kimberley = 12
Cape Town = 20

a. Draw a bar graph to represent this data.

b. What is the range of this data?

………………………………………………………………………………………………………..
c. What is the median temperature?
………………………………………………………………………………………………………..
d. What is the mean temperature?
………………………………………………………………………………………………………..

Facilitator comments: Assessment:

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
29

I understand Questions that I still would like

Concept (SO1)
this concept to ask

Questions about sets of data that

can be dealt with through
statistical methods are identified
correctly.

Existing tables are understood

correctly through a proper
application of row and column
headings.

Raw data or statistics in the body

of tables are used correctly.

Effective methods to record and

organise data are used to solve
problems.

Calculations of statistics are

correct.

Appropriate statistics are used to

answer questions.

Scales used in graphical

representations and tables are
consistent with the data, are
correct, clear and appropriate to
the situation and target audience.

My Notes …
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .
...................................................................................
...................................................................................
...................................................................................
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Session 2 Im p l i c a t i on s r e s u l t i n g f r om
mod e l e d d a t a
After completing this session, you should be able to:
SO 2: Give opinions on the implications of the modelled
data for the required purpose.

In this session we will use the information given to us in graphs to

determine what it means and how it is useful to us by exploring the
following concepts:
determine the trend from a data model
justify the trend you have identified
explain a graph in written or oral format

2.1 The language of graphs

Graphs give us a lot of information that is relevant to our lives. When you
open up the newspaper, there is bound to be some form of a graph in it to
communicate a message to you or to prove a point that has been made.

Trends
Often we can determine the relationship between the data we have and the
events that occur.

Example

Rebecca has a small spaza shop in her community. She sells the usual
things such as bread, milk, cigarettes and sweets. One of the things that
she sells is ice cream. When it is hot, she sells more ice cream than when it
is cold. She decides to find out if there is a relationship between her ice-
cream sales and the temperature.

Rebecca carefully follows the weather report everyday and then records her
sales of ice-cream for the day – Rebecca’s shop is not open on a Sunday.

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Rebecca records the following information:

Week 1 Mo Tu We Th Fr Sa
Temp 30 32 28 25 29 31
Weather Sun Sun Sun Rain Sun Sun
Ice- 15 20 12 6 16 25
cream

Week 2 Mo Tu We Th Fr Sa
Temp 22 20 23 25 27 30
Weather Rain Rain Rain Sun Sun Sun
Ice- 3 0 3 5 9 22
cream

Week 3 Mo Tu We Th Fr Sa
Temp 33 32 33 31 30 29
Weather Sun Sun Sun Sun Sun Sun
Ice- 20 19 22 23 25 28
cream

Week 4 Mo Tu We Th Fr Sa
Temp 25 23 20 18 18 25
Weather Rain Rain Rain Rain Rain Sun
Ice- 5 4 2 0 0 11
cream

Rebecca decides to use a histogram to see what the relationship is between

the information that she has gathered.

35

30

25

20

15

10

0
Temp Ice-cream

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
32

Ice-
Temp
cream
Mo 30 15
Tu 32 20
We 28 12
Th 25 6
Fr 29 16
Sa 31 25
Mo 22 3
Tu 20 0
We 23 3
Th 25 5
Fr 27 9
Sa 30 22
Mo 33 20
Tu 32 19
We 33 22
Th 31 23
Fr 30 25
Sa 29 28
Mo 25 5
Tu 23 4
We 20 2
Th 18 0
Fr 18 0
Sa 25 11

The histogram looks confusing and she decides to redo the data on a
broken line graph:

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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35

30

25

20 Temp
15 Ice-cream

10

0
e

e
o

o
Fr

Fr

Fr

Fr
M

M
W

W
The broken line graph shows the similarity between the temperature and
the ice-cream sales. If you look at the temperature line, you can see that
on the first Thursday the temperature was about 25º and on this Thursday
Rebecca sold only 6 ice-creams. However, on the first Saturday the
temperature was 31º and she sold 25 ice creams.

You can see a similar curve in the ice-cream sales line as in the temperature
line. Rebecca should hope for hot sunny days to improve her ice-cream
sales.

We can now establish a trend:

• the hotter the temperature, the more the ice-cream that is sold
• the cooler the temperature, the less the ice-cream that is sold
• on a sunny day Rebecca sells more ice-cream
• on a rainy day Rebecca sells less ice-cream

Rebecca can take this information a step further. She can look at what the average
price of her ice-creams are, i.e.
• suckers R2.00
• chocolate ice-cream R3.50
• cones R5.00

Average = (2 +3,5 + 5) ÷ 3
= 10,5 ÷ 3
= R3.50

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She can now work out how much money she brings in with her ice-cream sales
alone:

Total Income = Ice-creams sold (one month) x average price of ice-cream:

Ice-creams sold
Week 1: 15 + 20 + 12 +6 +16 25 = 94
Week 2: 3 +0 +3 +5 +9 + 22 = 42
Week 3: 20 + 19 + 22 + 23 + 25 + 28 = 137
Week 4: 5 +4 +2 +0 +0 + 11 = 22
= 295

Rebecca can now calculate her income from ice-cream sales for this month:

Total income = 295 x 3.50

= R1 032.50

From this information Rebecca can:

• Determine her stock levels for ice-cream for one month
• Negotiate better bulk discount for ice-cream that she buys from the ice-
cream supplier
• Prepare for ice-cream sales by keeping an eye on the weather report

Should Rebecca do this over a period of 12 months, she is able to plan ahead for her
business.

My Notes …
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .
...................................................................................
...................................................................................
...................................................................................
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Example

Rebecca has summarized her monthly data for the past 12 months as follows:

Average Average Ice-cream

Month Temperature sold
January 27º 295
February 26º 290
March 25º 250
April 24º 200
May 21º 150
June 18º 100
July 16º 50
August 17º 75
September 19º 100
October 20º 150
November 25º 250
December 29º 300

Average Ice-cream sold

350
300
250
200
150
100
50
0
Jan Feb March April May June July Aug Sept Oct Nov Dec

Rebecca can see that over a period of one year, she sells more ice-cream in
summer, when it is hot, than in winter, when it is cold. She will therefore plan her
stock accordingly.

Please complete Activity My Notes …

3 at the end of the ....................................
session . ...................................
. ...................................
. ...................................
. ...................................

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3
Individual activity: My Name:
Complete the questions .......................
below My Workplace:
.......................
SO 2 My ID Number:

1. The pictograph below shows the number of hours of sunshine per month in
1998 from January to June in Cape Town.

Jan
Feb
March
April
May
June

= 1 Hr

a) Which month had the most hours of sunshine?

………………………………………………………………………………………………………..
b) Which month had the least hours of sunshine?
………………………………………………………………………………………………………..
c) Which month had 9 hours of sunshine?
………………………………………………………………………………………………………..
d) How many hours of sunshine did May have?
………………………………………………………………………………………………………..
e) How many hours of sunshine did June have?
………………………………………………………………………………………………………..
f) How many hours of sunshine were there altogether in the whole period
January to June?
………………………………………………………………………………………………………..

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2. In this bar graph the highest daily temperature for one week in a town is
shown.

Maximum temperature for one week inTown A

35
30
25
Temperature in 20
Degrees C 15
10
5
0
Mon Tue Wed Thurs Fri Sat Sun
Days of the week

a) Which was the hottest day of the week?

………………………………………………………………………………………………………..
b) Which was the coolest day of the week?
………………………………………………………………………………………………………..
c) What was the temperature on Friday?
………………………………………………………………………………………………………..
d) On which day was the temperature 29ºC?
………………………………………………………………………………………………………..
e) On which day was the temperature 31ºC?
………………………………………………………………………………………………………..
f) What was the average temperature for the week shown?
………………………………………………………………………………………………………..
………………………………………………………………………………………………………..
g) Is this the correct type of graph? Justify your answer.
………………………………………………………………………………………………………..
………………………………………………………………………………………………………..

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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3. This graph shows the number of baskets of tea leaves harvested in one week
by various workers.

John

Peter

Jack

Paul

Ben

0 10 20 30 40 50 60 70 80 90
Marks achieved

a) Who harvested the most tea?

………………………………………………………………………………………………………..
b) Who harvested the least tea?
………………………………………………………………………………………………………..
c) How many baskets full did Paul harvest?
………………………………………………………………………………………………………..
d) How many baskets full did peter harvest?
………………………………………………………………………………………………………..
e) Those who harvested less than 50 baskets got less pay. Who were
they?
………………………………………………………………………………………………………..

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
39

4. The graph underneath shows the amount of rainfall in a certain area from
Monday to Saturday.

60

50
Rainfall in mm

40

30

20

10

0
Mon Tue Wed Thurs Fri Sat Sun
Days of the Week

a) Which day had the most rainfall?

………………………………………………………………………………………………………..
b) Which day had the least rainfall?
………………………………………………………………………………………………………..
c) How much rainfall fell on Thursday?
………………………………………………………………………………………………………..
d) Which day had 52 mm of rainfall?
………………………………………………………………………………………………………..
e) What was the average rainfall for the 6 days?

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
40

5. The following stem-and-leaf diagram shows the total number of points scored
in a series of basketball games.

160 2
170 1
180 2, 7
190 5, 7, 2
200 9, 4, 8, 0
210 5, 9, 7, 0, 3, 3
220 4, 9

a) How many scores of 170 were registered?

………………………………………………………………………………………………………..
b) How many scores of 213 were registered?
………………………………………………………………………………………………………..
c) What was the lowest score?
………………………………………………………………………………………………………..
d) What was the highest score?
………………………………………………………………………………………………………..
e) What were the common most scores?
………………………………………………………………………………………………………..
f) Were most scores above or below 200?
………………………………………………………………………………………………………..

Facilitator comments: Assessment:

Version: 01 Version Date: July 2006

 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
41

I understand Questions that I still

Concept
this concept would like to ask

Verbal (written or oral) explanation of

findings is based on the representation
of the data.

Trends, group profiles and attitudes are

justified.

Appropriate information is extracted

from representations in order to answer
questions.

My Notes …
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .
...................................................................................
...................................................................................
...................................................................................
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .
...................................................................................
...................................................................................
...................................................................................
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .
...................................................................................
...................................................................................
...................................................................................
...................................................................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
...................................................................................
...................................................................................
...................................................................................
...................................................................................

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
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1. To what extent did you apply and adapt generic information you learned in
this module to your specific outlet in your work experience? Discuss and
describe.

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

2. What do you think was particularly helpful to you in your workplace

experience?

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

• Where do you need to improve?

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
43

• What will you charge?

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

3. Did the practical experience on-site make you want o adjust the theory you
learned? If so, what would you adjust and how would this change what you
would to in the future?

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
44

Assessment Feedback Form

Comments / Remarks

Feedback to learner on assessment:

Feedback from learner to assessor:

Learner’s Signature: Date:

Assessor’s Signature:
Date:

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and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
45

Am I ready for my test?

Check your plan carefully to make sure that you prepare in good time.
You have to be found competent by a qualified assessor to be declared
competent.
Inform the assessor if you have any special needs or requirements before the
agreed date for the test to be completed. You might, for example, require an
interpreter to translate the questions to your mother tongue, or you might need
to take this test orally.
Use this worksheet to help you prepare for the test. These are examples of
possible questions that might appear in the test. All the information you need
was taught in the classroom and can be found in the learner guide that you
received.
1. I am sure of this and understand it well
2. I am unsure of this and need to ask the Facilitator or Assessor to explain what it means

2. I
1. I am
Questions am
sure
unsure

Question 1

A farmer wants to see how well his sheep do on different feeds.

Before he starts his experiment, he determines the mass of his
sheep. The results are shown in the table below in kilograms:

65 72 54 58 67 92 74 77
83 68 73 81

70 95 56 74 85 66 93 60
78 60 82 77

76 85 59 71

a) Construct a frequency table to show these data.

b) What was the mass of the lightest sheep?
c) What was the mass of the heaviest sheep?
d) Comment on the distribution of masses.
e) Construct a stem-and-leaf plot and answer the
following questions.
f) The median.
g) The mode.
h) The mean (average) mass.

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
46

Question 2

This table shows how an agriculture student spends his day.

Activity College Sleeping Sports Eating Other

No. of
8 8 3 1 4
hours

a) Show this information on a pie chart.

b) Start by working out the fractions and then change it
to degrees.

Question 3

1) The following table shows a student’s Mathematics Test

results.

Geom Statist Graph Expon Factoriz Perce

Integers
etry ics s ents ation ntage

Test no. 1 2 3 4 5 6 7
%
obtained
52 67 74 60 74 85 94

a) Show this data on a Broken line graph.

b) What is the mean?
c) Which tests were above average?

Question 4

When you throw a dice, what is the probability to throw a:

a) Six.
b) Four
c) And even number.
d) A number larger than 4.

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Primary Agriculture NQF Level 2 Unit Standard No: 9009
47

Checklist for practical assessment …

Use the checklist below to help you prepare for the part of the practical
assessment when you are observed on the attitudes and attributes that you need
to have to be found competent for this learning module.

Answer Motivate your Answer

Observations
Yes or No (Give examples, reasons, etc.)

Can you identify problems and deficiencies

correctly?

Are you able to work well in a team?

Do you work in an organised and

systematic way while performing all tasks
and tests?

Are you able to collect the correct and

appropriate information and / or samples
as per the instructions and procedures that
you were taught?

Are you able to communicate your

knowledge orally and in writing, in such a
way that you show what knowledge you
have gained?

Can you base your tasks and answers on

scientific knowledge that you have learnt?

Are you able to show and perform the

tasks required correctly?

Are you able to link the knowledge, skills

and attitudes that you have learnt in this
module of learning to specific duties in
your job or in the community where you
live?

The assessor will complete a checklist that gives details of the points that are
checked and assessed by the assessor.
The assessor will write commentary and feedback on that checklist. They will
discuss all commentary and feedback with you.
You will be asked to give your own feedback and to sign this document.
It will be placed together with this completed guide in a file as part
of you portfolio of evidence.
The assessor will give you feedback on the test and guide you if there are
areas in which you still need further development.
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Primary Agriculture NQF Level 2 Unit Standard No: 9009
48

Paperwork to be done …
Please assist the assessor by filling in this form and then sign as instructed.

Learner Information Form

Apply basic knowledge of statistics and probability to influence the
Unit Standard use of data and procedures in order to investigate life related
problems.

Program Date(s)

Assessment Date(s)

Surname

First Name

Learner ID / SETA
Registration
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Version: 01 Version Date: July 2006

 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
49

Bibliography
Books:
Gray, D.E, 2004. Doing research in the real world. Sage . London.
‘Life skills’ by Edna Rooth

Terms & Conditions

This material was developed with public funding and for that reason this material
is available at no charge from the AgriSETA website (www.agriseta.co.za).

Users are free to produce and adapt this material to the

maximum benefit of the learner.

No user is allowed to sell this material whatsoever.

Version: 01 Version Date: July 2006

 Apply basic knowledge of statistics and probability to influence the use of data
and procedures in order to investigate life related problems
Primary Agriculture NQF Level 2 Unit Standard No: 9009
50

Acknowledgements
Project Management:
M H Chalken Consulting
IMPETUS Consulting and Skills Development

Donors:

South Cape College

Authenticator:
Ms C Almeida

Technical Editing:
Ms C Almeida

OBE Formatting:
Ms B Enslin

Design:
Didactical Design SA (Pty) Ltd

Layout:
Ms S Mallick

Version: 01 Version Date: July 2006

 All qualifications and unit standards registered on the National Qualifications Framework are public property.
Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this
material for profit. If the material is reproduced or quoted, the South African Qualifications Authority
(SAQA) should be acknowledged as the source.

SOUTH AFRICAN QUALIFICATIONS AUTHORITY

REGISTERED UNIT STANDARD:

Apply basic knowledge of statistics and probability to influence the use of data and
procedures in order to investigate life related problems

SAQA US ID UNIT STANDARD TITLE

9009 Apply basic knowledge of statistics and probability to influence the use of data and
procedures in order to investigate life related problems
SGB NAME REGISTERING PROVIDER
SGB for Math Literacy, Math, Math Sciences L 2 -4
FIELD SUBFIELD
Field 10 - Physical, Mathematical, Computer and Life Mathematical Sciences
Sciences
ABET BAND UNIT STANDARD TYPE NQF LEVEL CREDITS
Undefined Regular-Fundamental Level 2 3
REGISTRATION REGISTRATION START REGISTRATION END SAQA DECISION
STATUS DATE DATE NUMBER
Reregistered 2004-12-02 2007-12-02 SAQA 1657/04

PURPOSE OF THE UNIT STANDARD

This Unit Standard is designed to provide credits towards the mathematical literacy requirement of the NQF
at Level 2. The essential purposes of the mathematical literacy requirement are that, as the learner
progress with confidence through the levels, the learner will grow in:
. A confident, insightful use of mathematics in the management of the needs of everyday living to become
a self-managing person
. An understanding of mathematical applications that provides insight into
the learner`s present and future occupational experiences and so develop into a contributing worker

The ability to voice a critical sensitivity to the role of mathematics in a democratic society and so become a
participating citizen

People credited with this Unit Standard are able to:

Apply various techniques to organise and represent data in order to model situations for specific purposes.
Give opinions on the implications of the modelled data for the required purpose.

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING

The credit value is based on the assumption that people starting to learn towards this unit standard are
competent in

UNIT STANDARD RANGE

This unit standard includes the requirement to:

Identify issues suited to resolution by basic statistical methods.

Work with existing data.
Generate statistics through the use calculators and other available technology.
Represent data in the form of tables, charts and graphs.
Use statistics and representations of data to
Summarise real-life and or work related issues within the experience of the learner.
Give opinions on statistics and representations of data.
More detailed range statements are provided for specific outcomes and assessment criteria as needed.

Specific Outcomes and Assessment Criteria:

SPECIFIC OUTCOME 1
Apply various techniques to organise and represent data in order to model situations.
OUTCOME NOTES
Apply various techniques to organise and represent data in order to model situations for specific purposes.
OUTCOME RANGE
Techniques include:

Using a variety of methods to represent statistics including pie charts, bar graphs, stem and leaf plots;

Reading tables (e. g., the meaning of row and column headings and the relationship between age by
gender by province);

Extracting a suitable set of data from tables and databases (e. g., census data, tables in newspapers, HIV
data; weather data);

Recording and organising data into tables;

Calculating measures of centre and spread such as mean, median, mode, and range; the use of
Quartiles in classifying data items ("Measures of centre and spread" should be handled via examples, which
are directly related to the life or work
experiences of each learner. For example workers` wages and learners` test scores).

ASSESSMENT CRITERIA

ASSESSMENT CRITERION 1
1. Questions about sets of data that can be dealt with through statistical methods are identified correctly.

ASSESSMENT CRITERION 2
2. Existing tables are understood correctly through a proper application of row and column headings.

ASSESSMENT CRITERION 3
3. Raw data or statistics in the body of tables are used correctly.

ASSESSMENT CRITERION 4
4. Effective methods to record and organise data are used to solve problems.

ASSESSMENT CRITERION 5
5. Calculations of statistics are correct.

ASSESSMENT CRITERION 6
6. Appropriate statistics are used to answer questions.

ASSESSMENT CRITERION 7
7. Scales used in graphical representations and tables are consistent with the data, are correct, clear and
appropriate to the situation and target audience.
SPECIFIC OUTCOME 2
Give opinions on the implications of the modelled data for the required purpose.
OUTCOME RANGE
Purposes include:

Determining trends in societal issues such as crime and health;

Identifying relevant characteristics of target groups such as age range, gender, socio-economic group,
cultural belief, and performance;

Considering the attitudes or opinions of people on current issues relevant to the life experience of the
learners;

Determining weather patterns for a given region.

ASSESSMENT CRITERIA

ASSESSMENT CRITERION 1
1. Verbal (written or oral) explanation of findings is based on the representation of the data.

ASSESSMENT CRITERION 2
2. Trends, group profiles and attitudes are justified.

ASSESSMENT CRITERION 3
3. Appropriate information is extracted from representations in order to answer questions.

UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS

Providers of learning towards this unit standard will need to meet the accreditation requirements of the
GENFETQA.

Moderation Option:
The moderation requirements of the GENFETQA must be met in order to award credit to learners for this
unit standard.

UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE

The following essential embedded knowledge will be assessed through assessment of the specific
outcomes in terms of the stipulated assessment criteria. Candidates are unlikely to achieve all the specific
outcomes, to the standards described in the assessment criteria, without knowledge of the listed
embedded knowledge. This means that the possession or lack of the knowledge can be inferred directly
from the quality of the candidate `s performance against the standards.

Critical Cross-field Outcomes (CCFO):

UNIT STANDARD CCFO IDENTIFYING

Identify and solve problems using critical and creative thinking:
Give opinions, based on data and statistics, on a variety of problems and issues.

UNIT STANDARD CCFO COLLECTING

Collect, analyse, organise and critically evaluate information:
Select organise, and give opinions on statistics to make sense of situations related to the life or work of the
learner.
UNIT STANDARD CCFO COMMUNICATING
Communicate effectively:
Use everyday language and mathematical language to represent data, statistics and probabilities and to
communicate conclusions.

UNIT STANDARD CCFO CONTRIBUTING

Use mathematics:
Use mathematics to describe and represent situations and to solve life related problems.

UNIT STANDARD ASSESSOR CRITERIA

Assessors should keep the following general principles in mind when designing and conducting
assessments against this unit standard:

Focus the assessment activities on gathering evidence in terms of the main outcome expressed in the title
to ensure assessment is integrated rather than fragmented. Remember we want to declare the person
competent in terms of the title. Where assessment at title level is unmanageable, then focus assessment
around each specific outcome, or groups of specific outcomes.

Make sure evidence is gathered across the entire range, wherever it applies. Assessment activities should
be as close to the real performance as possible, and where simulations or role-plays are used, there should
be supporting
evidence to show the candidate is able to perform in the real situation.

Do not focus the assessment activities on each assessment criterion. Rather make sure the assessment
activities focus on outcomes and are sufficient to enable evidence to be gathered around all the
assessment criteria.

The assessment criteria provide the specifications against which assessment judgements should be made.
In most cases, knowledge can be inferred from the quality of the performances, but in other cases,
knowledge and understanding will have to be tested through questioning techniques. Where this is
required, there will be assessment criteria to specify the standard required.

The task of the assessor is to gather sufficient evidence, of the prescribed type and quality, as specified in
this unit standard, that the candidate can achieve the outcomes again and again and again. This means
assessors will have to judge how many repeat performances are required before they believe the
performance is reproducible.

All assessments should be conducted in line with the following well-documented principles of assessment:
appropriateness, fairness, manageability, and integration into work or learning, validity, direct, authentic,
sufficient, systematic, open and consistent.

UNIT STANDARD NOTES

N/A

All qualifications and unit standards registered on the National Qualifications Framework are public property. Thus the only
payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is
reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.