Question

Find the sample Standard deviation and the population standard deviation of the data set 17,37,56,16,12,16,19,45,14,37,21,26,43,46,42

Answer 1

1. 13.98

2. 14.47

Explanation:

The question is on sample standard deviation and population standard deviation

Arrange the data in increasing order

12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56

n=15

Find the mean of the data set

`mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15`

mean= 29.67 ⇒30

Find the deviations

You subtract the value of mean from each of the data set given

Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26

Find squares of deviations

= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676

Find sum of squares of deviations

`324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930`

1. Treating the data set to represent an entire population then;

Variance= sum of squares of deviation/number of data set

Variance= 2930/15 = 195.33

Population standard deviation = √195.33 = 13.98

2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14

Sample Variance=2930/14 =209.29

sample standard deviation= √209.29 = 14.47