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Grade 7 Mathematics Learner’s Book

INNODEMS

Section 5.1 Data handling

Subsection 5.1.1 Meaning of data

Data is a collection of facts such as numbers and measurements that we learn, make decisions or solve problems.
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An example of data in a classroom could be the information on finding out how many pens each group in the classroom has. Here is the data we collected:
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  1. Group Names: Group 1, Group 2, Group 3
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  2. Number of Pens:
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This information is considered data because counting pens helps us manage and organize our resources effectively. For instance, if one group needs more pens, we can identify which group has extra pens to share. You could use this data to figure out things like:
  • Which group has the most pens?
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  • How many pens are there in total?
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  • What is the average number of pens per group?
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Activity 5.1.1.

Work in groups
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(i) Each learner state their understanding of the term data.
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(ii) Search for the meaning of data from different sources.
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(iii) Discuss and compare with other groups.
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Learning point
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  • Data is a collection of facts such as numbers and measurements collected to represent information.
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Subsection 5.1.2 Collection of data

A collection of data refers to the process of gathering and assembling relevant pieces of information or facts from various sources for analysis or use.
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This data can be quantitative (numerical) or qualitative (descriptive) and is typically organized in a structured manner to allow for efficient examination or decision-making.
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Data collection can take many forms, such as:
  1. Surveys and questionnaires: Gathering responses from individuals
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  2. Experiments: Recording observations or measurements during controlled experiments.
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  3. Interviews: Collecting qualitative data through direct interactions.
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Activity 5.1.2.

Work in groups
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(i) Collect data on the number of classrooms in your school.
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(ii) Count the number of textbooks for each subject in your class.
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(iii) Collect data on the number of male and female in your class.
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(iv) Collect information on the number of left handed students in your class.
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(v) Discuss and compare with other groups.
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Learning point
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  • Data collected from different situations vary from each other.
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Subsection 5.1.3 Frequency distribution table

A frequency distribution table displays the frequency of each data set in an organized way.
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Frequency is the rate at which something occurs over a particular period of time or in a given sample.
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It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance.
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Activity 5.1.3.

Work in groups
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(i) Consider the following list showing the favourite fruits for learners.
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Table 5.1.1. Frequency distribution table
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Learner Fruit
Kemunto Banana
Otieno Apple
Kamau Apple
Esipisu Banana
Omar Guava
Sidika Apple
Nanjala Guava
Njoki Banana
Sagar Guava
Baraza Banana
Anyango Banana
Issa Banana
(ii) Represent the information in a table that has Fruit, Tally and Frequency.
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(iii) Compare and discuss with other groups.
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Learning points
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  1. A tally mark represents one unit. One mark represent a frequency of one.
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  2. A table having one unit and the number of times it occurs is a frequency table
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Example 5.1.2.

The height, in centimetres, of 30 tree seedlings were recorded as follows:
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15 20 18 15 20 15 16 14 20 14 12 14 15 16 10
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12 10 16 18 15 16 11 13 16 14 12 17 16 20 19
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Draw a frequency distribution table to represent this information.
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Solution.
Table 5.1.3. Frequency distribution table representing tree seedling
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Height Tally Frequency
10 // 2
11 / 1
12 /// 3
13 / 1
14 //// 4
15 ///// 5
16 ////// 6
17 / 1
18 // 2
19 / 1
20 //// 4
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Example 5.1.4.

In a quiz, the marks obtained by 20 students out of 30 are given as follows
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12,15,15,29,30,21,30,30,15,17,19,15,20,20,16,21,23,24,23,21
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Draw a frequency distribution table to represent this information.
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Solution.
Table 5.1.5. Frequency distribution table representing students marks
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Marks Tally Frequency
12 / 1
15 //// 4
16 / 1
17 / 1
19 / 1
20 // 2
21 /// 3
23 // 2
24 / 1
29 / 1
30 /// 3
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Subsection 5.1.4 Suitable scale for graphs of data

Activity 5.1.4.

work in groups
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(i) consider the table below
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Table 5.1.6.
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Marks Frequency
4 2
5 10
6 5
7 20
8 3
9 4
(ii) Determine a suitable scale you would use to draw a bar graph.
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(iii) Discuss and compare with other groups.
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Learning point
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  • A suitable scale should be chosen in such a way that data is easy to plot and easy to read.
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Subsection 5.1.5 Pictographs of data

A pictograph is a type of data visualization that uses pictures or symbols to represent and convey data.
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Each picture or symbol typically represents a specific quantity or value, making it easier to understand and interpret data.
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Activity 5.1.5.

Work in groups
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(i) Consider the table shown
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Table 5.1.7. Favourite musical instrument
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🎸 😊😊😊😊
🥁 😊😊
🎹 😊😊😊
🪈 😊😊😊😊😊
key: 😊represents four children
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(ii) Write down the number of children whose favourite musical instrument is: (a) Guitar (b) Drum (c) Keyboard (d) Flute
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(iii) Discuss and compare with other groups.
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Learning point
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  • A pictograph is a representation of data using images, icons and symbols.
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Example 5.1.8.

The following pictograph shows the number of students who were absent from a class in a given week.
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Table 5.1.9.
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Days Number of absentees
Monday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
Tuesday
Wednesday 🧍🏼🧍🏼
Thursday 🧍🏼🧍🏼🧍🏼
Friday 🧍🏼
Key: 🧍🏼represents one student
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(a) On which day were the maximum number of students absent?
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(b) Which day had full attendance?
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Solution.
(a) Monday
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(b) Tuesday
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Example 5.1.10.

The table shows the number of students present in a class of 32 in a week.
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Table 5.1.11.
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Days Number of students present
Monday 24
Tuesday 20
Wednesday 28
Thursday 32
Friday 28
Represent the information in a pictograph.
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Solution.
Key: 🧍🏼represents 4 students
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Table 5.1.12.
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Days Number of students present
Monday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
Tuesday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
Wednesday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
Thursday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
Friday 🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼🧍🏼
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Example 5.1.13.

The pictograph below shows the number of books borrowed from a school library over five days
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Table 5.1.14.
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Days of the week Number of books borrowed 📙 = 5 vehicles
Monday 📙📙📙📙📙
Tueday 📙📙📙📙
Wednesday 📙📙📙📙📙📙
Thursday 📙📙📙
Friday 📙📙📙📙📙📙📙
Answer the following questions:
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(a) How many books were borrowed on Monday?
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(b) On which day were the most books borrowed?
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(c) How many books were borrowed in total during the week?
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(d) How many more books were borrowed on Friday compared to Thursday?
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Solution.
(a) \(5\times 10=50\) Therefore, 50 books were borrowed on Monday
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(b) Friday
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(c) Total Books Borrowed:
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Total = \(50+40+60+30+70 = 250\)
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Therefore, \(250\) books were borrowed throughout the week.
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(d) More Books Borrowed on Friday than Thursday:
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Subsection 5.1.6 Bar graphs of data

Bar graph is a visual representation of data where individual bars (rectangular shapes) are used to represent the values or frequencies of different categories.
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The length or height of each bar corresponds to the value it represents, making it easy to compare different categories.
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Activity 5.1.6.

Work in groups
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(i) Consider the table below showing the number of loaves of bread sold in a school canteen in a week.
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Table 5.1.15.
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Day Monday Tuesday Wednesday Thursday Friday
Number of leaves sold 100 250 200 150 300
(ii) Choose a suitable scale to represent the data on a graph.
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(iii) Using bars, represent the data on a graph.
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(iii) Compare and discuss with other groups.
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Example 5.1.16.

The table below shows monthly expenses of a household in a certain month.
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Table 5.1.17. Monthly expenses of a household in a certain month
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Item Expenditure (Ksh)
House Rent 3000
Food 3500
Education 2000
Electricity 500
Transport 1500
Represent the data on a bar graph
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Solution.
(i) Choose a suitable scale for the length of bars, for example, let 1cm represent Ksh. 500.
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(ii) Work out the Length of the bars as shown.
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Table 5.1.18. Frequency table
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Items Expenditure (Ksh.) No. of squares making the height
House rent 3000 6
Food 3500 7
Education 2000 4
Electricity 500 1
Transport 1500 3
(iii) Draw a bar graph for the data.
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Example 5.1.19.

The bar graph shown represents favourite games for a number of learners.
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  1. Find the number of learners whose favourite game was:
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    (a) Soccer
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    (b) Netball
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    (c) Volleyball
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  2. Find the total number of learners whose favourite game was soccer, netball or volleyball.
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Solution.
  1. (a) 15 learners
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    (b) 10 learners
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    (c) 20 learners
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  2. 45 learners
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Checkpoint 5.1.20.

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Subsection 5.1.7 Pie charts of data

A pie chart is a type of graph representing data in a circular form, with each slice of the circle representing a fraction or proportionate part of the whole. All slices of the pie add up to make the whole equaling 100 percent and 360 degrees.
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Activity 5.1.7.

work in groups
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(i) Consider the table below
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Table 5.1.21.
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Mode of Transport Bus Bicycle On foot Car
Number of students 200 100 80 20
(ii) Draw a circle of suitable radius.
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(iii) Divide the circle into sectors to represent the information.
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(iv) Compare and discuss with other groups.
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Learning point
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  • Frequency is represented by the size of a sector in a pie chart.
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Example 5.1.22.

The Table below shows different types of animals kept by a farmer.
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Table 5.1.23.
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Animals Cows Goats Sheep Pigs
Number of animals 12 24 18 6
Draw a pie chart to represent this information
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Solution.
The total angle at the centre of a circle is \(360^\circ\text{.}\) The central angles of sectors representing the animals are fractions of \(360^\circ\text{.}\) The total number of animals in the farm is 12+24+18+6 = 60.
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Table 5.1.24.
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Animal No. of animals Fraction Fraction of 360 degrees
Cows \(12\) \(\frac{1}{5}\) \(\frac{1}{5}\times360^\circ = 72^\circ \)
Goats \(24\) \(\frac{2}{5}\) \(\frac{2}{5}\times360^\circ = 144^\circ\)
Sheep \(18\) \(\frac{3}{10}\) \(\frac{3}{10}\times360^\circ = 108^\circ\)
Pigs \(6\) \(\frac{1}{10}\) \(\frac{1}{10}\times360^\circ = 36^\circ\)
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Example 5.1.25.

Murunga is a fruit farmer. The table below shows the number of fruit trees on Murunga’s farm.
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Table 5.1.26. Pie chart to represent the number of trees
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Fruit trees Oranges Lemons Apples Pawpaws
Number of trees 600 300 150 150
Draw a pie chart to represent the number of trees.
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Solution.
Total number of trees is \(600\)+\(300\)+\(150\)+\(150\)=\(1200\)
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Oranges \(\frac{600}{1200}\times 360^\circ = 180^\circ\)
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Apples \(\frac{150}{1200}\times 360^\circ = 45^\circ\)
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Pawpaws \(\frac{150}{1200}\times 360^\circ = 45^\circ\)
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Lemons \(\frac{300}{1200}\times 360^\circ = 90^\circ\)
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Checkpoint 5.1.27.

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Subsection 5.1.8 Interpretation of pie charts

Activity 5.1.8.

Work in groups
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(i) Consider the pie chart representing different types of crops planted in a 6 hectare farm shown.
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(ii) Find and record the information represented in the pie chart.
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(iii) Discuss and share with other groups.
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Learning point
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  • Information represented in a pie chart is obtained using the total number of items represented and the angles expressed as fractions of \(360^\circ\text{.}\)
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Example 5.1.28.

The pie chart shows types of vehicles that passed by a school gate within one hour.
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If the number of vehicles that passed by the school were 72, find how many lorries, pickups and cars passed by the school gate.
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Solution.
The number of lorries were \(\frac{120^\circ }{360^\circ }\times 72=24\)
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The number of pick ups were \(\frac{90^\circ }{360^\circ }\times 72=18\)
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The number of cars were \(\frac{150^\circ }{360^\circ }\times 72=30\)
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Example 5.1.29.

The pie chart below represents careers that \(56\) learners would love to pursue in future.
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(a) How many learners want to pursue Law?
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(b) How many learners want to pursue Fine Art?
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(c) How many learners want to pursue Medicine?
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(d) How many learners want to pursue Teaching?
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Solution.
Measure the angle representing each career.
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(a) Number of learners who want to pursue Law is \(\frac{90^\circ }{360^\circ }\times 56=14\)
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(b) Number of learners who want to pursue Fine Art is \(\frac{45^\circ }{360^\circ }\times 56=7\)
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(c) Number of learners who want to pursue Medicine is \(\frac{135^\circ }{360^\circ }\times 56=21\)
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(d) Number of learners who want to pursue Teaching is \(\frac{45^\circ }{360^\circ }\times 56=7\)
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Number of learners who prefer Medicine to Teaching is \(21-7=14\)
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Subsection 5.1.9 Line graphs of data

Line graph of data is a visual representation of data where individual data points are connected by straight lines, showing how a variable changes over time or across a continuous scale, typically with the horizontal axis representing time and the vertical axis representing the measured values.
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It is used to identify trends and patterns in data over a period of time.
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Activity 5.1.9.

Work in groups
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  1. Consider the table shown on the amount of recorded rainfall in a place for a period of six months.
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    Table 5.1.30. Amount of Rainfall for a period of six months
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    Month Jan. Feb. March. April. May. June.
    Amount of Rainfall(mm) 50 70 80 150 140 110
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  2. Represent the information on a line graph.
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  3. Share and discuss with other groups.
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Learning point
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  • In line graphs, points are connected with straight lines to represent changes in values over a period of time.
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Example 5.1.31.

The table shown represents the sale of motorcycles by a company from the month of June to December 2021
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Table 5.1.32.
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Month June July Aug. Sept. Oct. Nov Dec.
No. of motocycles 10 40 30 20 30 40 50
Draw a line graph to represent the information
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Solution.
Scale 1 cm represents 10 motorcycles.
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Example 5.1.33.

The table below shows recorded average temperature of a place in a week.
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Table 5.1.34. Average temperature in a week
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Day Mon Tue Wed Thur Fri Sat Sun
Average temperature \(16.5^\circ C\) \(15^\circ C\) \(17^\circ C\) \(18^\circ C\) \(20^\circ C\) \(15.5^\circ C\) \(14^\circ C\)
Solution.
Scale 1 cm represents \(5^\circ C\)
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Example 5.1.35.

A Learner measured changes in the length of a flag post’s shadow at different times. She recorded the lengths as shown. Below is a representation of the line graph
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Table 5.1.36. Time vs Lengths in metres
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Time 7:00 a.m 9:00 a.m 11:00 a.m 1:00 p.m
Lengths in metres 6 m 4 m 2 m 0 m
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