Statistics, Year 8: more practice：全部卡片
整套按顺序列出——孩子看到之前，您可以先通读一遍。
- In a survey of 30 pupils, 6 chose swimming as their favourite sport. What angle is the swimming slice of a pie chart?
72°
提示Find the angle for one pupil first.
为什么360° ÷ 30 = 12° per pupil, and 6 × 12° = 72°.
- Three slices of a pie chart measure 120°, 90° and 100°, and the pie has only one other slice. What angle is the fourth slice?
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°.
- A pie chart shows 80 pupils. The 'bus' slice has an angle of 45°. How many pupils take the bus? (number only)
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.
- One slice of a pie chart has an angle of 36°. What percentage of the data does it show? (number only)
10
提示Compare the slice with a full turn of 360°.
为什么36/360 = 1/10 = 10%.
- A frequency table shows score 1 with frequency 2, score 2 with frequency 3 and score 3 with frequency 5. What is the mean score? (number only)
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.
- When finding the mean from a frequency table, what do you work out in an extra column before adding up?
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.
- A shoe shop wants to know which size to order the most of. Which average is the most useful?
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.
- What is the midpoint of the class 20 ≤ x < 30? (number only)
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.
- Why is it hard to compare a segment from the middle of the stack across the bars of a compound bar chart?
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.
- The mean of 3, 4, 5, 6 and 7 is 5. If the 7 is replaced by 37, what is the new mean? (number only)
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.
1★ KS3-MATH-STA-0068
2★ KS3-MATH-STA-0069
3★ KS3-MATH-STA-0070
4★ KS3-MATH-STA-0071
5★ KS3-MATH-STA-0072
6★ KS3-MATH-STA-0073
7★ KS3-MATH-STA-0074
8★ KS3-MATH-STA-0075
9★ KS3-MATH-STA-0076
10★ KS3-MATH-STA-0077