Centre & Spread — Practice
One number for the middle is never enough, because two very different groups can share an average.
What these questions 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.
Problem 1
Find the mean of 4, 8, 10, 14.
Worked answer
9
36 ÷ 4 = 9
Problem 2
Find the mean of 3, 7, 8.
Worked answer
6
18 ÷ 3 = 6
Problem 3
Find the median of 3, 7, 9, 12, 15.
Worked answer
9
Five values, so the third
Problem 4
Find the mode of 2, 3, 3, 5, 7, 3.
Worked answer
3
3 appears three times
Problem 5
Find the range of 12, 19, 4, 15.
Worked answer
15
19 - 4 = 15
Problem 6
Find the median of 5, 1, 9, 3.
Worked answer
4
1,3,5,9
3+52 = 4
Problem 7
Find the median of 8, 2, 11, 5, 7.
Worked answer
7
2,5,7,8,11
The third is 7
Problem 8
Find the mean of 3, 4, 4, 5, 14.
Worked answer
6
30 ÷ 5 = 6
Problem 9
Find the mean absolute deviation of 4, 8, 10, 14.
Worked answer
3
Mean 9
Distances 5,1,1,5
12 ÷ 4 = 3
Problem 10
The mean of five numbers is 12. Find their total.
Worked answer
60
12 × 5 = 60
Problem 11
Prices are $210k, $220k, $230k, $240k and $1.2m. Which describes a typical house better?
- The median
- The mean
- The range
- The mode
Worked answer
The median
Mean $420k describes no house on the street
Problem 12
Find the mean absolute deviation of 2, 4, 6, 8.
Worked answer
2
Distances 3,1,1,3
8 ÷ 4 = 2
Problem 13
Four numbers have mean 7. Three of them are 5, 6 and 9. Find the fourth.
Worked answer
8
28 - 20 = 8
Problem 14
Two classes both average 80. Class A has MAD 1.2, class B has MAD 12. Which is true?
- Class B is far more spread out
- They are identical
- Class A is more spread out
- Cannot tell
Worked answer
Class B is far more spread out
Class B has students far from the middle
Problem 15
Find the median of 4, 4, 7, 9, 10, 12.
Worked answer
8
7+92 = 8
Problem 16
Adding one very large value to a data set will
- raise the mean much more than the median
- raise the median more
- change neither
- lower both
Worked answer
raise the mean much more than the median
The mean does; the median barely moves