Question

Find the standard deviation for the group of data items.
Stems
Leaves
2
6   
3
1 6
4
1 6

Answer 1

The data are 26, 31, 36, 41, 46.
Mean = (26+31+36+41+46)/5 = 180/5 = 36.

Squared deviations: (26−36)^2=100, (31−36)^2=25, (36−36)^2=0, (41−36)^2=25, (46−36)^2=100.
Sum of squares = 250.

- Population variance = 250/5 = 50, so population standard deviation = sqrt(50) = 5√2 ≈ 7.071.
- Sample variance = 250/(5−1) = 62.5, so sample standard deviation ≈ sqrt(62.5) ≈ 7.906.

(Use the population value 5√2 ≈ 7.07 if these 5 items are the entire group.)