Charts and diagrams

• A pictogram uses symbols, with a key such as "one circle = 4 people". Half a circle is 2 people.
• A bar chart has bars of equal width, with gaps between them for separate categories.
• A dual bar chart puts two bars side by side for each category, to compare two groups.
• A composite bar chart stacks the parts of each group into one bar.

Example: in a pictogram, one circle stands for 4 people. A row has 3½ circles. How many people is that?

1. 3 circles = 3 × 4 = 12 people
2. Half a circle = 2 people
3. 14 people

Always label the axes and give a pictogram a key.

A pie chart shows how a total is split up. The whole circle, 360°, is the total.

Angle = frequency ÷ total × 360°

Example: 60 students chose their favourite sport: football 25, tennis 10, swimming 15 and other 10. Find each angle.

1. Each student is 360 ÷ 60 = 6°
2. Football: 25 × 6 = 150°; tennis: 10 × 6 = 60°
3. Swimming: 15 × 6 = 90°; other: 10 × 6 = 60°

Check: 150 + 60 + 90 + 60 = 360.

Example: a pie chart shows 90 people. A sector has an angle of 72°. How many people does it show?

1. 72 ÷ 360 × 90 = 18 people

1. Choose the stems (usually the tens digits) and write them in a column.
2. Write each value's units digit as a leaf next to its stem.
3. Redraw it with the leaves in order, and add a key.

Example: draw a stem-and-leaf diagram for 34, 27, 41, 38, 22, 35, 29.

1. Stems: 2, 3 and 4
2. Ordered leaves:

3. Key: 2 | 2 means 22

A frequency polygon shows grouped data. Plot each frequency at the midpoint of its class, and join the points with straight lines.

Example: draw a frequency polygon for the times in the table: 0 < t ≤ 10: 5; 10 < t ≤ 20: 12; 20 < t ≤ 30: 9; 30 < t ≤ 40: 4.

1. Midpoints: 5, 15, 25 and 35
2. Plot (5, 5), (15, 12), (25, 9) and (35, 4)
3. Join them with straight lines

Frequency polygons are useful for comparing two sets of data on the same axes.

To compare two sets of data, compare:

1. an average (mean or median): which is bigger on average?
2. a measure of spread (range or interquartile range): which is more consistent?

Write each comparison in the context of the question.

Example: in a test, class A had a mean of 62 and a range of 30. Class B had a mean of 58 and a range of 15. Compare the classes.

1. On average, class A scored higher, because its mean (62) is higher than class B's (58)
2. Class B's scores were more consistent, because its range (15) is smaller than class A's (30)