Statistics, Year 8: more practice

72°

HintFind the angle for one pupil first.

The why360° ÷ 30 = 12° per pupil, and 6 × 12° = 72°.

50°

HintAngles around a point add up to a whole turn.

The why120 + 90 + 100 = 310, and 360 − 310 = 50, so the fourth slice is 50°.

10

HintTurn the angle into a fraction of the whole circle.

The why45/360 = 1/8, and 1/8 of 80 is 10.

10

HintCompare the slice with a full turn of 360°.

The why36/360 = 1/10 = 10%.

2.3

HintMultiply each score by its frequency, add them, then divide by the number of values.

The why(1×2 + 2×3 + 3×5) ÷ (2 + 3 + 5) = (2 + 6 + 15) ÷ 10 = 23 ÷ 10 = 2.3.

Each score multiplied by its frequency

HintThink about what stands for the total of one row's values.

The whyEach row's total is score × frequency. Adding these gives the total of all the data, and dividing by the sum of the frequencies gives the mean.

The mode

HintWhich size do the shop's customers choose most often?

The whyThe mode is the most common value, so it tells the shop which size is bought most often. A mean shoe size might not be a real size at all.

25

HintHalfway between the two ends of the class.

The why(20 + 30) ÷ 2 = 25. The midpoint stands in for every value in the class when you estimate a mean.

The segments do not start from the same baseline

HintThink about where each segment begins.

The whyOnly the bottom segment starts from zero. Middle segments sit on top of other segments of different heights, so their sizes cannot be compared directly by eye.

11

HintFind the new total, then divide by the number of values.

The whyThe new total is 3 + 4 + 5 + 6 + 37 = 55, and 55 ÷ 5 = 11. The median stays at 5, so one outlier drags the mean but hardly moves the median.