Question

what is the sample standard deviation of data set 15, 18, 16, 18, 15,13, 14, 18, 16, 10?

Answer 1

In ascending order = 10, 13, 14, 15, 15, 16, 16, 18, 18, 18

Mean = 10 + 13 + 14 + 15 + 15 + 16 + 16 + 18 + 18 + 18/ 10

= 153/10

= 15.3

Subtract the mean from all the values and then square them

10 - 15.3 = (-5.3)² = 28.09

13 - 15.3 = (-2.3)² = 5.29

14 - 15.3 = (-1.3)² = 1.69

15 - 15.3 = (-0.3)² = 0.09

15 - 15.3 = (-0.3)² = 0.09

16 - 15.3 = (0.7)² = 0.49

16 - 15.3 = (0.7)² = 0.49

18 - 15.3 = (2.7)²  = 7.29

18 - 15.3 = (2.7)² = 7.29

18 - 15.3 = (2.7)² = 7.29

Sum up all and divide by n-1, where n = 10 (number of samples)

= sum/ n - 1

= 58.1/9

= 6.45

Now, variance = 6.45

Standard deviation = sqrt 6.45

= 2.53

Sorry if any calculation mistake..