Mathematics
Grade 7 • Unit 13: Data Collection and Organization
LESSON 13.3
Data Presentation Tools
Table of Contents
Introduction 1
Test Your Prerequisite Skills 2
DepEd Competency 3
Objectives 3
Warm-Up! 3
Learn about It! 5
Let’s Practice 14
Check Your Understanding 20
Key Points 21
Bibliography 22
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Lesson 13.3
Data Presentation Tools
Fig. 1. Rainy Weather
Introduction
How do people know that the months from June to December are the times when the
Philippines experiences rain, while the months from March to May are the times when it
experiences hot weather? This predictable pattern results from careful and thorough data
gathering and research that can be represented through data presentation tools.
In this lesson, you will learn about the different types of data presentation tools and their
uses. You will also create appropriate graphs based on the context of the given data.
1
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Test Your Prerequisite Skills
Before you get started, answer the following items on a separate sheet of paper. This will
help you assess your prior knowledge and practice some skills that you will need in studying
this lesson. Show your complete solution.
1. Plot the following points on the Cartesian plane.
a. (5,10), (0, 2.5), (3, 10), (10, 9)
b. (5, 10), (5, 20), (10, 15), (15, 25)
2. Using the graph below, answer the following questions:
a. What is the graph all about?
b. How many categories are in the graph? Name them.
c. What type of movie is the favorite of most students?
2
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
DepEd Competency
At the end of the lesson, you should be able to use appropriate graphs to
represent organized data: pie chart, bar graph, line graph, histogram, and ogive
(M7SP-IVd-e-1).
Objectives
At the end of this lesson, you should be able to do the following:
● Correctly use different graphs for their specific purposes.
● Properly create a graph based on the given data.
Warm-Up!
Birthday Month
Materials
● 3R baby picture
● pen, paper
● cartolina
● coloring materials
Instructions
1. Form at least two groups.
2. On a cartolina, create a table similar to the table below.
3
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Month Picture(s) Month Picture(s)
January July
February August
March September
April October
May November
June December
3. For each group, paste your picture beside your birthday month in the table below.
4
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
4. How many students have their birthdays in every month?
January: __________ May: __________ September: __________
February: __________ June: __________ October: __________
March: __________ July: __________ November: __________
April: __________ August: __________ December: __________
5. What is the most common birthday month? _____________
What is the least common birthday month? _____________
6. What method will you use to present the data that you have gathered from your
classmates?
Learn about It!
Let us once again recall our scenario about Rocky. Let us help him graphically present the
data he gathered.
Category Frequency Relative Frequency Percentage
Apples 4 0.20 20%
Bananas 2 0.10 10%
Grapes 3 0.15 15%
Mangoes 4 0.20 20%
Oranges 4 0.20 20%
Strawberries 3 0.15 15%
Total 20 1.00 100%
5
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Essential Question
Why do we need to use graphs in presenting a set of data?
One way we can present the data is by using a bar graph.
Definition 3.1: A bar graph uses the height or length of the bar
to represent how often a particular category
was observed.
To draw a bar graph, plot the frequency against the categories as shown below.
Fruit Preference
We can also present the data using a pie chart.
Definition 3.2: A pie chart is a circular graph that shows how
the categories are distributed.
6
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
To draw a pie chart, assign one sector of a circle to each category. The angle of each sector
should be proportional to the relative frequency in that category. Since one full circle has 360°,
we can find the angle for each category by multiplying the relative frequency by 360°.
Category Frequency Relative Frequency Percentage Angle
Apples 4 0.20 20% 0.20 × 360° = 72°
Bananas 2 0.10 10% 0.10 × 360 = 36°
Grapes 3 0.15 15% 0.15 × 360 = 54°
Mangoes 4 0.20 20% 0.20 × 360 = 72°
Oranges 4 0.20 20% 0.20 × 360 = 72°
Strawberries 3 0.15 15% 0.15 × 360 = 54°
Total 20 1.00 100% 360°
You may color your pie chart to distinguish the categories from each other.
Fruit Preference
7
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Now let us assume that Rocky recorded the temperature outside for five days and observed
the data below.
Day 1 2 3 4 5
Temperature 36°C 34°C 31°C 29°C 33°C
The data set is a time series since the variable is recorded over time. Time series is best
presented on a line graph.
Definition 3.3: A line graph uses dots and lines to discern a
pattern or trend that could continue into the
future.
This pattern could then be used to predict future events. To draw a line graph, plot the time
(horizontal) against the observed phenomena (vertical) and then connect them using lines.
5-Day Temperature Record
8
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Another way to graph quantitative data is by using a histogram.
Definition 3.4: A histogram resembles a bar graph and shows
how often measurements fall in a particular
class or subinterval.
Let us consider the following data gathered by Rocky about the age of his neighbors:
15 25 36 41 22 44 33 80 33 56
39 18 28 65 72 63 5 48 66 75
To construct a histogram, we must construct a frequency distribution table for grouped data:
1. Choose the number of classes, usually between 5 and 20, to be used. The more data
you have, the more classes you should use.
2. Calculate the class width (𝒘) using the following formula:
range
𝑤=
desired no. of classes
highest value − lowest value
=
desired no. of classes
We round up the class width to a whole number and determine the class intervals or
the value that comprise one category using this value.
3. Record the number of scores (frequency) that fall under each class interval.
9
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
4. Construct a statistical table containing the classes, class interval, frequencies, and
relative frequencies.
5. Construct the histogram like a bar graph. Place the class intervals on the horizontal
axis while and frequencies on the vertical axis. Note that there should be no space in
between the bars unless there is no value that falls under a certain interval.
Let us say we want to have eight classes for the data given.
range = highest value − lowest value
= 80 − 5
= 75
range
class width (𝑤) =
desired no. of classes
75
=
8
= 9.375
≈ 10
This means that we have 10 values that could fall under each class interval.
Thus, if we start from 1, the first class interval must be until 10. The second interval must be
11–20, and so on until we create 8 intervals. Note that the smallest value must be included in
the first class, and the highest value must be included in the last class.
Next, we construct a statistical table and record the frequency of data that fall under the
classes.
10
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Class Class Interval Frequency Relative Frequency
1 1–10 1 0.05
2 11–20 2 0.10
3 21–30 3 0.15
4 31–40 4 0.20
5 41–50 3 0.15
6 51–60 1 0.05
7 61–70 3 0.15
8 71–80 3 0.15
Lastly, we construct the histogram using the table above.
Age of Rocky’s Neighbors
We could also present the data above using an ogive.
11
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
To get the cumulative frequency of a class, we must add its frequency to all the preceding
frequencies. The first frequency is also the first cumulative frequency.
Class Class Frequency Relative Cumulative Frequency
Interval Frequency
1 1–10 1 0.05 1
2 11–20 2 0.10 1+2=3
3 21–30 3 0.15 1+2+3=6
4 31–40 4 0.20 1 + 2 + 3 + 4 = 10
5 41–50 3 0.15 1 + 2 + 3 + 4 + 3 = 13
6 51–60 1 0.05 1 + 2 + 3 + 4 + 3 + 1 = 14
7 61–70 3 0.15 1 + 2 + 3 + 4 + 3 + 1 + 3 = 17
8 71–80 3 0.15 1 + 2 + 3 + 4 + 3 + 1 + 3 + 3 = 20
Note that the cumulative frequency of the last class is the total frequency. In the given
example, the last cumulative frequency is 20, and the total frequency is also 20.
Now we can construct an ogive by plotting the points and connecting them with lines using
the cumulative frequencies on the vertical axis and the class intervals on the horizontal axis.
Each point must be plotted at the upper limit of the class boundary.
12
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Essential Question
How do we choose the best type of graph suited to present a data?
13
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Let’s Practice
Example 1
Describe the graph below and interpret its data.
Sports Preference
Solution
The graph above is a bar graph and is about the sports preference of certain number of
individuals.
Basketball is the sport with the highest frequency, which has 6, followed by soccer with a
frequency of 5, followed by badminton with a frequency of 4, and volleyball with 3 as the
frequency.
By adding the frequencies, we can determine the number of persons asked about their sports
preferences. That is, 6 + 5 + 4 + 3 = 18 persons.
14
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Try It Yourself!
Describe the graph below and interpret its data.
Favorite Pet of 20 Grade 6 Students
Example 2
Angela created a pie chart to display the percentage of people who watch different kinds of
movies as shown. What kind of movie is least watched?
Solution
The least watched are the romantic comedy movies since it has the smallest portion in the
chart.
15
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Try It Yourself!
Arrange the ethnic groups from least to highest population in the Philippines.
Ethnic Groups in the Philippines
Example 3
Suppose we collect information on the ages (in years) of 45 students selected from the Basic
Education department of the school. The ages of the students are listed below. Construct the
frequency distribution table with 6 classes and the corresponding ogive to present the results.
5 12 10 16 8 9 15 8 9
10 15 8 7 8 7 14 6 10
11 11 9 7 13 12 12 13 11
15 13 6 10 14 14 5 14 7
6 12 8 9 14 8 9 9 5
16
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Solution
The frequency distribution table is as follows:
Class Class Interval Frequency Cumulative Frequency
1 5-6 6 6
2 7-8 10 16
3 9-10 10 26
4 11-12 7 33
5 13-14 8 41
6 15-16 4 45
Try It Yourself!
Construct a frequency distribution table of the weight of your classmates (in kilograms).
Use an ogive to present your data.
17
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Real-World Problems
Example 4
A scholarship committee administered a qualifying test to 40 students for a scholarship
grant. The scores of the students are listed below.
120 130 125 110 100 80 132 135 131 149
121 130 150 78 90 137 115 120 125 110
111 99 78 130 130 90 95 98 99 110
100 101 98 89 90 78 72 79 138 91
If students whose scores belong to the top 30 are qualified, what was the lowest possible
score for a qualifier? Construct a frequency distribution table with eight classes and the
corresponding ogive to present the results.
Solution
Construct a frequency distribution table first. Let us use 8 class intervals as required.
range = highest − lowest
= 150 − 72
= 78
range
class width (𝑤) =
desired no. of classes
78
=
8
= 9.75
≈ 10
18
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Class Class Frequency Cumulative
Interval Frequency
1 71–80 6 6
2 81–90 4 10
3 91–100 8 18
4 101–110 4 22
5 111–120 4 26
6 121–130 7 33
7 131–140 6 39
8 141–150 1 40
Construct the ogive using the frequency distribution table.
Qualifying Test Result
Based on the given problem, only the top 30 students will qualify. Therefore, the lowest 10
students will not receive the scholarship grant. Looking at the ogive above, we can see that
19
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
the lowest 10 students are those who scored 90 and below. Thus, the lowest score possible
for a qualifier is 91.
Try It Yourself!
Anita will be presenting the data on the student’s status in her school. The data gathered
from 50 selected students are listed below. In the table, F, SO, J, and SE are the abbreviations
for freshman, sophomore, junior, and senior, respectively. What is the best way to present
her data? What graph is not applicable to the data of Anita?
Check Your Understanding
1. If you want to present the percentage of a student’s weekly expenses, which chart
is the most appropriate to use?
2. The ogive below shows the scores of 20 students in a 25-item quiz. If the passing
score is 15, how many passed the quiz?
20
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Quiz Result
3. For her statistics project, Nina gathered information about the final grades of her
classmates in mathematics. Construct a histogram for the grades she obtained
using a frequency distribution with five classes. The grades are listed below.
79, 79, 79, 80, 84, 84, 84, 85, 86, 87, 87, 88, 89, 89, 90,
91, 92, 92, 92, 93, 94, 94, 95, 95, 96, 96, 96, 97, 97, 98
Key Points
• A bar graph uses the height or length of the bar to represent how often a particular
category was observed.
• A pie chart is a circular graph that shows how the categories are distributed.
• A line graph uses dots and lines to discern a pattern or trend that could continue into
the future.
• A histogram resembles a bar graph and shows how often measurements fall in a
particular class or subinterval.
• An ogive is a cumulative frequency graph.
21
Mathematics
●
Grade 7 • Unit 13: Data Collection and Organization
Bibliography
"Types of Graphs." Byju’s The Learning App. Retrieved 28 August 2019 from
http://bit.ly/2Pi9CZQ
22
