What is the Standard deviation of...?

Ordinary speaking the average = sum(allvalues)/number of values = 36.22.

Variance = sum((value-average)^2)/number of values = 7893.556/9 = 877.062, and

standard deviation = sqrt(variance) = 29.62.

However, if your set of values is a sample of 9 values taken from the large set of equally distributed values, then the so called sample mean is the same as the above average. However, the sample variance = sum((value-average)^2)/(number of values - 1) = 7893.556/8 = 986.6944, and st. dev. = 31.412.

x (x-36.22)^2

23 174.83

56 391.16

84 2282.72

1 1240.60

25 125.94

5 974.83

45 77.05

8 796.49

79 1829.94

== ==

326 7893.56

Count = 9

Mean = 36.22 = 326 /9

Sample Variance = 986.69 = 7,893.56 /8 ; note the denominator is n-1

Sample 'SD = SQRT(986.69) = 31.41