Question

find the standard deviation and mean for each set of numbers

Suppose you are interested in genealogy, and want to try to predict your potential longevity by using the ages at death of your ancestors. You find out the ages at death for the eight great-grandparents of your mother and your father. Suppose the ages (in numerical order) are as follows. mother's great-grandparents: 81, 83, 83, 84, 84, 85, 85, 87 father's great-grandparents: 30, 50, 75, 83, 85, 90, 94, 98

Answer 1

First Set :

The numbers are 81, 83, 83, 84, 84, 85, 85, 87

Mean = sum of all numbers / total numbers

          = (81 + 83 + 83 + 84 + 84 + 85 + 85 + 87) / 8

          = 84

Variance = (sum of square of all numbers / total numbers) - mean²

               = (81² + 83² + 83² + 84² + 84² + 85² + 85² + 87²) / 8 - 84²

               = 7058.75 - 7056

               = 2.75

Standard deviation = $\sqrt{variance}$

                               =

V2.75

                               = 1.66

Therefore, the mean is 84 and standard deviation is 1.66

Second Set :

The numbers are 30, 50, 75, 83, 85, 90, 94, 98.

Mean = sum of all numbers / total numbers

          = (30 + 50 + 75 + 83 + 85 + 90 + 94 + 98) / 8

          = 75.625

Variance = (sum of square of all numbers / total numbers) - mean²

               = (30² + 50² + 75² + 83² + 85² + 90² + 94² + 98²) / 8 - 75.625²

               = 6209.875 - 5719.141

               = 490.73

Standard deviation = $\sqrt{variance}$

                               = $\sqrt{490.73}$

                               = 22.15

Therefore, the mean is 75.625 and standard deviation is 22.15