Centre & Spread — Drills
Centre & Spread has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Median — Two kinds of centre: the balance point, and the middle value.
- MAD — Mean absolute deviation — the average distance from the mean; a measure of spread.
- Mode — The value that appears most often.
- Range — The largest value minus the smallest.
- Mean absolute deviation — The average distance of the values from the mean.
Mean
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the mean of 11, 16, 19, 10, 19.
Worked answer
15
Total = 75
75 ÷ 5 = 15
Problem 2
Find the mean of 16, 12, 11.
Worked answer
13
Total = 39
39 ÷ 3 = 13
Median
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the median of 16, 15, 14, 25.
Worked answer
15.5
Sorted: 14, 15, 16, 25
Average the middle two: 15.5
Problem 2
Find the median of 13, 3, 8, 9, 15.
Worked answer
9
Sorted: 3, 8, 9, 13, 15
The middle value is 9
Range
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the range of 22, 27, 37, 3.
Worked answer
34
37 - 3 = 34
Problem 2
Find the range of 32, 21, 18, 34.
Worked answer
16
34 - 18 = 16
Mad
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the mean absolute deviation of 0, 4, 12, 16.
Worked answer
6
Mean = 8
Distances: 8, 4, 4, 8
244 = 6
Problem 2
Find the mean absolute deviation of 6, 9, 15, 18.
Worked answer
4.5
Mean = 12
Distances: 6, 3, 3, 6
184 = 4.5
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
4 numbers have mean 13. All but one are 14, 17, 16. Find the missing one.
Worked answer
5
Total = 13 × 4 = 52
52 - 47 = 5
Problem 2
5 numbers have mean 10. All but one are 7, 12, 7, 6. Find the missing one.
Worked answer
18
Total = 10 × 5 = 50
50 - 32 = 18