Mean, median and mode
Answers are for parents and teachers.
1
Classes 0–, 10–, 20–, 30–40 have frequencies 2, 8, 6, 4. Find the mean.
10 + 120 + 150 + 140 = 420; 420 ÷ 20 = 21.
2
Classes 0–, 10–, 20–, 30–40 have frequencies 3, k, 5, 2 and the mean is 20. Find k. (Midpoints 5, 15, 25, 35.)
210 + 15k = 20 × (10 + k) gives 10 = 5k, so k = 2.
3
The cumulative values are 0, 6, 16, 34, 40 at 0, 10, 20, 30, 40. Find the median.
Rank 20; class 20–30 (16 to 34); 20 + 4 ÷ 18 × 10 ≈ 22.2.
4
Frequencies 4, 10, 6 in the classes 10–, 20–, 30–40. Find the modal class and the mode.
Modal class 20–; d₁ = 10 − 4 = 6 and d₂ = 10 − 6 = 4; mode 20 + 10 × 6 ÷ 10 = 26.
5
Eight shops sell a toy at 20 LE and one shop sells it at 100 LE. Which is better to describe the usual price: the mean or the median? Why?
The median, 20 LE. The mean (260 ÷ 9 ≈ 28.9 LE) is pulled up by the one high price.