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

15

HintWhat fraction of a full turn is the slice?

The why90° is a quarter of 360°, and a quarter of 60 is 15.

1/5

HintCompare the angle with a full turn.

The why72 ÷ 360 = 1/5, because 5 × 72 = 360. A slice is always its angle out of 360.

No — not without the class totals

HintHalf of what, in each case?

The whyHalf 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°

HintEach person is worth the same number of degrees.

The why360 ÷ 120 = 3° per person, and 30 × 3 = 90°. Or notice that 30 out of 120 is a quarter of the circle.

2

HintLook for the largest frequency, then read across.

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

1.9

HintMultiply each score by how often it occurs before adding.

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

11

HintIt is the middle one, with equal numbers either side.

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

1

HintFind the position of the middle value, then count through the frequencies.

The whyThere 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

HintCheck which class includes its lower end.

The whyThe 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

HintYou only know which class each one fell in.

The whyGrouping 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

HintSomeone could be 149.9 cm tall.

The whyMeasured 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

HintA fair comparison needs boxes of one size.

The whyWith 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

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

The whyPutting 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

HintEach bar is built up from parts.

The whyIt 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

HintIt unlocks the meaning of the colours.

The whyWithout it, two colours or shadings mean nothing. A chart also needs a title and labelled axes.

A dual bar chart

HintChoose the one where both bars start from the baseline.

The whySide-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.