Statistics, Year 8: pie charts, frequency tables and bar charts

15

提示What fraction of a full turn is the slice?

为什么90° is a quarter of 360°, and a quarter of 60 is 15.

1/5

提示Compare the angle with a full turn.

为什么72 ÷ 360 = 1/5, because 5 × 72 = 360. A slice is always its angle out of 360.

No — not without the class totals

提示Half of what, in each case?

为什么Half of a class of 30 is 15, but half of a class of 20 is 10. Pie charts show proportions, so equal slices need not mean equal counts.

90°

提示Each person is worth the same number of degrees.

为什么360 ÷ 120 = 3° per person, and 30 × 3 = 90°. Or notice that 30 out of 120 is a quarter of the circle.

2

提示Look for the largest frequency, then read across.

为什么The mode is the score that occurs most often. The highest frequency is 5, and it belongs to a score of 2.

1.9

提示Multiply each score by how often it occurs before adding.

为什么The total score is 1 × 3 + 2 × 5 + 3 × 2 = 19, and there are 3 + 5 + 2 = 10 scores. 19 ÷ 10 = 1.9.

11

提示It is the middle one, with equal numbers either side.

为什么(21 + 1) ÷ 2 = 11. The 11th value has ten values below it and ten above it.

1

提示Find the position of the middle value, then count through the frequencies.

为什么There are 11 values, so the median is the 6th. The first four are 0s, and the 5th, 6th and 7th are 1s.

10 ≤ h < 20

提示Check which class includes its lower end.

为什么The sign < 10 leaves 10 out of the first class; the sign 10 ≤ puts it in the second. Each value belongs to exactly one class.

The exact individual values

提示You only know which class each one fell in.

为什么Grouping makes a long list easy to read and to chart, but you can no longer tell whether a value in 10 ≤ h < 20 was 10.1 or 19.9.

Height is continuous, so any value must have a class

提示Someone could be 149.9 cm tall.

为什么Measured data can take any value. Classes such as 140–149 and 150–159 would leave a height of 149.5 with nowhere to go.

Giving every class an equal width

提示A fair comparison needs boxes of one size.

为什么With unequal classes, a wide class can look popular just because it is wide. Equal widths let the frequencies be compared directly.

A dual bar chart

提示Its name comes from the Latin for 'two', like 'duet'.

为什么Putting the two bars next to each other makes it easy to compare the two years month by month. It is also called a comparative bar chart.

A compound (stacked) bar chart

提示Each bar is built up from parts.

为什么It shows totals clearly, and how each total is made up. It is also called a composite bar chart. The upper sections are harder to compare, as they do not start from a common line.

A key

提示It unlocks the meaning of the colours.

为什么Without it, two colours or shadings mean nothing. A chart also needs a title and labelled axes.

A dual bar chart

提示Choose the one where both bars start from the baseline.

为什么Side-by-side bars begin at one level, so their heights can be compared at a glance. Stacked bars are better when the totals matter most.