Data Presentation: Pie Charts – JSS3 Mathematics Lesson Note (Third Term)

A pie chart is a circle divided into sectors, where the size of each sector shows how often an item occurs in a set of data.

Behavioural objectives

By the end of the lesson, students should be able to:

1. arrange data in ranking order;
2. prepare a frequency table from a set of data;
3. calculate the angle of each sector of a pie chart;
4. draw a pie chart with a protractor;
5. say which item in a set of data is the most or least frequent.

What is statistics?

Statistics is the study of the collection, presentation and interpretation of data.

• Collection: gathering facts or figures, such as test scores or the number of vehicles in accidents.
• Presentation: showing the data in an ordered way, such as a table or chart.
• Interpretation: reading the table or chart to answer questions.

This lesson covers three parts of data presentation:

1. Ranking
2. Frequency table
3. Pie chart

What are the key terms in data presentation?

Data are facts or figures collected for a study.

• Frequency: the number of times a value or item appears in the data.
• Tally: a stroke used to count items one by one, with the fifth stroke crossing the first four.
• Sector: a slice of a circle, bounded by two radii and an arc.
• Total frequency: the sum of all the frequencies.

What is ranking?

Ranking order means arranging data from the highest to the lowest, or from the lowest to the highest.

• Descending order: from the highest to the lowest, as in 10, 9, 8, 7.
• Ascending order: from the lowest to the highest, as in 6, 7, 8, 9.

Example: 10, 9, 8, 8, 7, 7, 6, 6 are in ranking order.

What is a frequency table?

A frequency table shows the number of times each value appears.

How do you make a frequency table?

1. List each different value once, in ranking order.
2. Go through the data and make a tally stroke beside each value as you meet it.
3. Count the tallies for each value and write the number as its frequency.
4. Add the frequencies to get the total, and check it equals the number of items in the data.

Example: the marks 10, 9, 8, 8, 8, 7, 7, 6, 6 give this table. The total frequency is 9.

Worked example: ranking and frequency table

Some MGJSS students scored these grades in a mathematics test:

C, B, D, A, C, C, E, B, D, F, B, D, E, C, A, C, D, B

Rank order: A, A, B, B, B, B, C, C, C, C, C, D, D, D, D, E, E, F

Frequency table:

The total frequency is 2 + 4 + 5 + 4 + 2 + 1 = 18 students.

How do you draw a pie chart?

To draw a pie chart, calculate the angle of each sector as frequency ÷ total frequency × 360°, then draw the sectors with a protractor.

1. Rank the data and make a frequency table.
2. Find the total frequency.
3. Calculate the angle of each sector: frequency ÷ total × 360°.
4. Add the angles and check that they make 360°.
5. Draw a circle with a pair of compasses and mark its centre.
6. Draw one radius from the centre to the edge.
7. Place the protractor on this radius and mark the first angle. Draw the second radius.
8. Start from the new radius and repeat for each remaining sector.
9. Label each sector with its item and angle, or shade each differently and add a key.
10. Give the chart a title.

Angles for the grades example

Total number of students = 18

Check: the angles add up to 360°. Now draw the pie chart with a protractor.

How do you read a pie chart?

The largest sector shows the most frequent item, and the smallest sector shows the least frequent item.

• Most frequent: in the grades example, C has the largest sector (100°), so it is the most common grade.
• Least frequent: F has the smallest sector (20°), so it is the least common grade.
• Equal sectors: A and E both have 40°, so they have the same frequency.

What are a bar chart and a pictogram?

A bar chart uses bars of equal width whose heights show frequencies, and a pictogram uses pictures or symbols to show frequencies.

Bar chart

1. Draw a horizontal axis for the items and a vertical axis for the frequency.
2. Choose an equal scale on the vertical axis.
3. Draw one bar for each item, with equal widths and equal gaps.
4. Make each bar as high as its frequency, then label both axes and add a title.

Pictogram

1. Choose a simple symbol, for example one shoe.
2. Decide how many items one symbol stands for, and write this in a key.
3. Draw the number of symbols that matches each frequency.

Evaluation

The table below shows vehicles involved in serious accidents in Abuja.

1. How many vehicles were recorded?
2. Which type of vehicle had the worst record?
3. Which type of vehicle had the safest record?
4. Draw a bar chart of the data.
5. Represent the data in a pie chart.

Assignment

1. The data below shows the shoe sizes of men.
   

   Shoe size	6	7	8	9	10
   Frequency	4	5	9	4	2

   1. How many men are in the group?
   2. If you own a shoe shop, which size of shoes will you order most?
   3. Draw a pictogram.
   4. Draw a bar chart.
   5. Draw a pie chart.
2. The scores of students in a CA are as follows: 3, 0, 5, 2, 1, 4, 3, 2, 1, 1, 2, 3, 1, 2, 0, 3, 2, 1, 2
   1. Prepare a frequency tally table.
   2. How many students have the highest mark?
   3. How many students have the lowest mark?
3. In Abuja, the numbers of bedrooms in 50 houses chosen at random are as follows: 2, 5, 3, 5, 4, 7, 6, 3, 7, 4, 6, 3, 4, 3, 2, 5, 3, 5, 6, 6, 1, 4, 5, 6, 8, 7, 5, 3, 5, 1, 3, 5, 3, 3, 4, 2, 4, 5, 3, 3, 2, 1, 3, 4, 3, 1, 2, 4, 0, 3
   1. Prepare a frequency table of the distribution.
   2. Represent the data on a bar chart and a pie chart.
   3. Which number of bedrooms is the most frequent?
   4. Which number of bedrooms is the least frequent?