The sample standard deviation is calculated as:
[tex]s=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}}[/tex]
Where:
xi is the value of each sample
x(bar) is the mean of the sample
n is the number of samples
The dataset is 6, 7, 13, 11, 13
First, calculate the mean:
[tex]\bar{x}=\frac{6+7+13+11+13}{5}=\frac{50}{5}=10[/tex]
Now compute the differences between each data and the mean:
6 - 10 = -4
7 - 10 = -3
13 - 10 = 3
11 - 10 = 1
13 - 10 = 3
Square each result above:
(6 - 10)^2 = 16
(7 - 10)^2 = 9
(13 - 10)^2 = 9
(11 - 10)^2 = 1
(13 - 10) = 9
Sum the results above:
16 + 9 + 9 + 1 + 9 = 44
Calculate the standard deviation:
[tex]s=\sqrt{\frac{44}{4}}=\sqrt{11}=3.32[/tex]
The standard deviation is 3.32
