standard deviation

Question

Find the standard deviation of the data set. Round your answer to the nearest tenth.

65, 75, 40, 68, 80, 50, 56, 65

Answer 1

Mean of these numbers = 65+75+40+68+80+50+56+65/8

                                    = 498/8

                                    = 62.25

To calculate the numbers standerd deviation, first compute the difference of the each data point

from the mean, and sqare the result of each.

(65-62)^2 = 3^2 = 9

(75-62)^2 = 13^2 = 169

(40-62)^2 = (-22)^2 = 484

(68-62)^2 = 6^2 = 36

(80-62)^2 = 18^2 = 324

(50-62)^2 = (-12)^2 = 144

(56-62)^2 = (-6)^2 = 36

(65-62)^2 = 3^2 = 9

Next compute the mean of these values and take the sqare root.

= 9+169+484+36+324+144+36+9/8

= 1211/8

= 151.3

Sqare root of 151.3 is nearest to 12

The standard deviation of the data set. Round  to the nearest tenth of the data set,

65, 75, 40, 68, 80, 50, 56, 65 is 12