Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data.6,9,7,5,7,5,5,5,6,37Range: _____________Population Variance: ______________Population Standard Deviation: ___________

Answer 1

Range = 32

Variance = 87.4

Standard deviation = 9.3

Explanation:

Range is the difference between the largest and smallest numbers.

Range = 37 - 5 = 32

Variance is the average of the sum of squared differences between values and their mean.

So mean = sum of values ÷ 10

Mean= 92/10=9.2

Therefore Variance = [(6-9.2)² + (9-9.2)² + ... + (37-9.2)²] ÷ 10

= 87.36

Standard deviation= square root of variance

= √87.36

= 9.3