Question

What is the standard deviation and its meaning in the sample of customer ages? 48, 76, 30, 39, 51, 40, 63, 66, 27

a16.8 which means that many of the ages will be within this value of the average age

b16.8 which means that many of the ages will be around the square of this value

c15.8 which means that many of the ages will be around this value

d15.8 which means that many of the ages will be within half of this value of the average age

Answer 1

Number of samples in the data is 9

Mean of the data is,

mean = (48 + 76 + 30 + 39 + 51 + 40 + 63 + 66 + 27) / 9 = 48.89

Variance of the sample of customer ages is,

var = [(48 - 48.89)² + (76 - 48.89)² + (30 - 48.89)² + (39 - 48.89)² + (51 - 48.89)² + (40 - 48.89)² + (63 - 48.89)² + (66 - 48.89)² + (27 - 48.89)² ] / (9 - 1) = 280.6111

Standard deviation of the data is, $\sqrt{280.6111}$ = 16.8

Many of the data samples lie within one standard deviation of mean values. So, the correct answer is,

a16.8 which means that many of the ages will be within this value of the average age