Question

Find the sample standard deviation and the population standard deviation of the data set. 70, 58, 70, 37, 58, 47, 58, 76, 77, 67, 66, 77, 33, 74, 57

Answer 1

From the Data set given, we will solve for population standard deviation using the formula.
standard deviation = 1/n[
`\sqrt({x} -mean)^(2)`
mean = sum of all data/number of data
mean =925/15
mean=61.67
x

Answer 2

The formula for the sample standard deviation (denoted as s) and the population standard deviation (denoted as the greek letter sigma ∅) is shown in the picture where,

x is each entry of data
overbar x or ∪ is the mean or average
n or N is the number of data which is 15

They are just basically the same except for the denominator. First, let's determine the mean

overbar x or ∪ = (70+58+70+37+58+47+58+76+77+67+66+77+33+74+57)/15 = 61.7

The numerator would be
[(70-61.7)^2+(58-61.7)^2+(70-61.7)^2+(37-61.7)^2+(58-61.7)^2+....]
and so on and so forth.

The denominator for the sample is n-1 = 14, while the denominator for the population is n=15. Substituting the formula:

s=13.94
∅=13.47