Statistics, Year 8: more practice

72°

提示Find the angle for one pupil first.

为什么360° ÷ 30 = 12° per pupil, and 6 × 12° = 72°.

50°

提示Angles around a point add up to a whole turn.

为什么120 + 90 + 100 = 310, and 360 − 310 = 50, so the fourth slice is 50°.

10

提示Turn the angle into a fraction of the whole circle.

为什么45/360 = 1/8, and 1/8 of 80 is 10.

10

提示Compare the slice with a full turn of 360°.

为什么36/360 = 1/10 = 10%.

2.3

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

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

Each score multiplied by its frequency

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

为什么Each 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

提示Which size do the shop's customers choose most often?

为什么The 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

提示Halfway between the two ends of the class.

为什么(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

提示Think about where each segment begins.

为什么Only 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

提示Find the new total, then divide by the number of values.

为什么The 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.