»
of the decimal point as the stem for each observation.
et up @ relative frequency distribution
frequency 09!
The following
in 2 controlled laboratory experiment.
St@™ and lead plot for the life in years of the fuel pump using the digit
uct the frequency histogram, relative frequency polygon and the cumulative
ata represent the length of life in seconds of 50 fruit flies to a new spray
7 | 2 | 10 9 23 | 3 | 12 | 19 | 18 | 24
2 4 6 9 [3] 6 | 7 | | 3 [| 7
we | %@ | 8 | 3 | 3 | 3] 9 | 7 | 0 | 1 |
3 | 7 | @ i 7 | | 4.| # |-19 | | 8 |
7 | | 5 4 | 15 | 10 | 9 6 iu 15 |
2) Construct e double-stem and lead plot for the life span of the fruit using the stems
0*,0-, 1", 1_, 2", 2_, and 3° such that the stems are coded by the symbols * and
~ are associated respectively, with leaves 0 through 4, and 5 through 9.
b) Set up a relative frequency distribution.
c) Construct the frequency histogram, relative frequency polygon and the cumulative
frequency ogives.
Session 4 :
Measures of Central Tendency and Dispersion
By the end of ths session, you should be able to
1. Define. @ustrate. and distnguish the different measures of central tere,
Gispersion for grouped and ungrouped data
2. Interpret the computations for grouped and ungrouped data
Lecture:
iG
MEASURES OF CENTRAL TENDENCY
ontrolies
oe
"Give an example of a real-world use.
69
25 Suppose you surveyed 40 people about their daily screen’ time in hours Ys
found that most people fall into the 4~6 hour range.
a) What kind of data distribution does this suggest?
) How would a frequency histogram show this result visually?
Part D. Problem Solving (15 points each)
1) The following scores represent the final examination grade for an elementary sta
B jue (9 (32 [rea 2 aro CURE
80 | 7 | 81 95 | 41 | 65 | 92 | 85 55
62 | 10 | 64 [| 75 [ 78 | 25 | 80 | 98 81
la | a[ 8 54 | 54 | 72 | 8 | 62 74
| 84 | 90 15
34 | «67 17 82 62 | 74 | 63 | 80 85
a) Construct a stem and lead plot for the examination grades in which are thes:
are 1, 2,3, ...,9.
6) Set up a relative frequency distribution.
c) Construct the frequency histogram, relative frequency polygon and the cumu:
frequency ogives.
2) The following data fepresent the ‘enon Of life in years, measured to the nearest
of 30 similar fuel pumps:
'ead plot for the life in years of the fuel pump using the digit
point as the stem for each observation
UENCy distribution
cy histogram, relative frequency polygon and the cumulative
present the length of life in seconds of 50 fruit flies to a new spray
d laboratory experiment.
20 10 9 23 13 12 19 ig | 24
“4 6 3 [| 6 | 7 | 0 | 3 | 7
Q
18 8 13 3 2 | 3 |
7 rT i 2 40 4.127 1.419 | 6 ~/)~=«=8
10. A LaDIe Use I UIYGINee Udial IY Udo.
16.A cumulative graph that uses the upper class boundaries: s
17.A plot that keeps original data values while organizing them by fee value:
2 SNS HNN,
18. The percentage of total data falling into a class:
19. The number of times a data value or class occurs:
20. The sum of all previous frequencies up to a certain class: _
Part C. Short Answer / Essay (4 points each) (20 points)
ng bnefly and completely
Zing raw Gata into a frequency table important in statistics?
ograms and ogives differ in terms of what they show and how they
22. How do hist
are interpreted?
23.A dataset contains the following 10 values:
40, 15, 18, 12, 14, 17, 16, 15, 13, 11
a) Create a stem-and-leaf plot for this data.
b) What is the mode of the dataset?
24.When should you use cumulative frequency graphs (ogives) in data analysis?
Give an example of a real-world use.
69
2S Suppose you surveyed 40 people about their daily screen’ time in hours. ¥,,
found that most people fall into the 4-6 hour range.
a) What Kind of data distribution does this suggest?
b) How would a frequency histogram show this result visually?
a. Bar graph
b. Frequency polygon
© Cumulative frequency graph
d. Scatter plot
8. A relative frequency of 0.2 means
a, 20% of the total observations fall in that class:
b. 2 observations belong to that class
c. The cumulative frequency is 2
d. The class is the modal class
9. Ahistogram differs from a bar graph because
a. Ithas gaps between bars
b. It shows frequency, not categories
c. It shows trends over time
d. It uses percentages
10.What is the most common class or interval in a data set called?
a. Mean class
b. Median class
c. Modal class
d. Average range
Part B. Identification (1 point each) [10 points}
Write the correct term that matches the definition.
11.A visual representation of data using bars with no gaps:___
12.A table that shows each data point and how often itoccurs:
13.A graph that uses midpoints and frequency to connect dots;
, 14. The value halfway between the lower and upper boundaries of a class:
15.A table used to organize data into classes and frequencies:
46.A cumulative graph that uses the upper class boundaries:
17.A plot that keeps original data a while organizing them by place value
18. The percentage of total data falling into a class: =
49. The number of times a data value or class occurs: —_
20. The sum of all previous frequencies up to a certain class: _
B-
Part C. Short Answer / Essay (4 points each) (20 points]
Anewer the following bnefly and completely
21 Why \s organizing raw data into a frequency table important in statistics?
rams and ogives differ in terms of what they show and how they
wll Sal Tos! Ba)
Activity:
Part A. Multiple Choice (1 point each) [10 points]
Choose the best answer. Write the letter of your choice.
4. What is the main purpose of a frequency distribution table?
a. Predict future outcomes
b. Summarize large data sets
c. Create histograms
d. Eliminate outliers
2. Ina stem-and-leaf plot, the “stem” represents:
a. The average
b. The largest digit
c. The last digit
d. The leading digit(s)
3. The cumulative frequency shows
a. The number of data points in each class
b. The total number of frequencies
c. The percentage of values
d. The running total of frequencies
4, What is the midpoint of the class interval 20-29?
a. 24.5
b. 25
c. 20
d. 29
5. Which graph is best used to show relative percentages of categories?
a. Histogram
b. Pie chart
c. Ogive
d.. Polygon
6. What graphical tool uses upper class boundaries and cumulative frequency?
a. Frequency polygon
b. Histogram
c. Ogive
d, Pie chart
7. Which type of graph best shows the shape of a data distribution?
a, Bar graph
b. Frequency polygon
¢. Cumulative frequency graph
d. Scatter plot
8. A relative frequency of 0.2 means
a, 20% of the total observations fall in that class
b. 2 observations belong to that class
¢. The cumulative frequency is
d. The class is the modal class
9. A histogram differs from a bar graph because
a. It has gaps between bars
