Every card in Statistics, Year 8: more practice
The whole deck, in order — so you can read it through before your child ever sees it.
- In a survey of 30 pupils, 6 chose swimming as their favourite sport. What angle is the swimming slice of a pie chart?
72°
HintFind the angle for one pupil first.
Why360° ÷ 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°
HintAngles around a point add up to a whole turn.
Why120 + 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
HintTurn the angle into a fraction of the whole circle.
Why45/360 = 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
HintCompare the slice with a full turn of 360°.
Why36/360 = 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
HintMultiply each score by its frequency, add them, then divide by the number of values.
Why(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
HintThink about what stands for the total of one row's values.
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.
- A shoe shop wants to know which size to order the most of. Which average is the most useful?
The mode
HintWhich size do the shop's customers choose most often?
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.
- What is the midpoint of the class 20 ≤ x < 30? (number only)
25
HintHalfway between the two ends of the class.
Why(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
HintThink about where each segment begins.
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.
- 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
HintFind the new total, then divide by the number of values.
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.
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
Keep what you learn
Here, nothing is saved. In your child’s own sky every card is scheduled — it comes back just before they’d forget it — and the professor who wrote it is one tap away.