Answer:
The standard deviation of given data is 12.36
Step-by-step explanation:
We are given the following data in the question:
40, 12, 17, 25, 9, 46, 13, 22, 16,7
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{207}{10} = 20.7[/tex]
Sum of squares of differences =
372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1
[tex]\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36[/tex]
Thus, the standard deviation of given data is 12.36
