Mean, mode, median and deviation
Answers are for parents and teachers.
1
Find the mean, mode and median of 5, 9, 6, 7, 5, 8, 5, 7.
The sum is 52 so the mean is 6.5; the mode is 5; in order: 5, 5, 5, 6, 7, 7, 8, 9, and the median is (6 + 7)/2 = 6.5.
2
With xᵢ = 0, 1, 2, 3 and nᵢ = 5, 8, 4, 3, find the mean and the median.
n = 20; the sum is 0 + 8 + 8 + 9 = 25, so the mean is 1.25. The cumulative frequencies are 5, 13: the 10th and 11th terms are 1, so the median is 1.
3
Find the standard deviation of 1, 3, 5, 7.
x̄ = 4; the squares are 9, 1, 1, 9 with sum 20; sₙ = √(20/4) = √5.
4
Ages: 11–15 — 3 people, 16–20 — 5 people, 21–25 — 2 people. Find the approximate mean age.
Midpoints 13, 18, 23: (3 · 13 + 5 · 18 + 2 · 23)/10 = 175/10 = 17.5.
5
Two athletes have mean score 8 and standard deviations 0.4 and 1.5. Which is more consistent, and why?
The first: a small standard deviation means the results lie close to the mean.