Answer:
The standard deviation of this data set a sample from the population is equal to 94.9
Step-by-step explanation:
We have 20 observations in total or in the population and we want to know the standard deviation of this data set.
The standard deviation formula to a sample from the population is:
[tex]S=\sqrt{\frac{sum(x-Am)^2}{n-1}}[/tex] (1)
Where:
S: Standard deviation
sum: Summation
x: Sample values
Am: Arithmetic mean
n: Number of terms, in this case 20
Now, we need to know the arithmetic mean of the sample values
[tex]Am=\frac{25+45+73+16+34+98+34+45+26+2+56+97+12+445+23+63+110+12+17+41}{20}[/tex]
[tex]Am=\frac{1274}{20}\\ Am=63.7[/tex]
To know the standard deviation we need to have the summation of each term minus the arithmetic mean squared.
[tex](x-Am)^2[/tex] of each term:
[tex](25-63.7)^2=1497.69\\(45-63.7)^2=349.69\\(73-63.7)^2=86.49\\(16-63.7)^2=2275.29\\(34-63.7)^2=882.09\\(98-63.7)^2=1176.49\\(34-63.7)^2=882.09\\(45-63.7)^2=349.69\\(26-63.7)^2=1421.29\\(2-63.7)^2=3806.89\\(56-63.7)^2=59.29\\(97-63.7)^2=1108.89\\(12-63.7)^2=2672.89\\(445-63.7)^2=145390\\(23-63.7)^2=1656.49\\(63-63.7)^2=0.49\\(110-63.7)^2=2143.69\\(12-63.7)^2=2672.89\\(17-63.7)^2=2180.89\\(41-63.7)^2=515.29[/tex]
The summation of each term minus the arithmetic mean squared is: 171128.2
Now, we can find the standard deviation with the equation (1)
[tex]S=\sqrt{\frac{sum(x-Am)^2}{n-1}}[/tex]
[tex]S=\sqrt{\frac{171128.2}{20-1}}\\S=\sqrt{\frac{171128.2}{19}}\\S=\sqrt{9006.75} \\S=94.9[/tex]
The standard deviation is equal to 94.9
