Question

Find the standard deviation for the group of data items.
Stems
Leaves
3
6   
4
2 6
5
2 6

Answer 1

Interpret the stem-and-leaf as the numbers 36, 42, 46, 52, 56.

Mean = (36+42+46+52+56)/5 = 232/5 = 46.4

Squared deviations:
- (36−46.4)^2 = 108.16
- (42−46.4)^2 = 19.36
- (46−46.4)^2 = 0.16
- (52−46.4)^2 = 31.36
- (56−46.4)^2 = 92.16
Sum = 251.20

Population variance = 251.20/5 = 50.24 → population SD = sqrt(50.24) ≈ 7.09
Sample variance = 251.20/4 = 62.80 → sample SD = sqrt(62.80) ≈ 7.93

(Use ≈7.09 if treating the data as the entire population; use ≈7.93 if treating it as a sample.)