The standard deviation of given data set rounded to the hundredth place is 2.55
Given data set is: 9, 11, 12, 16
The mean of the data set is 12.
The formula for standard deviation is written as:
[tex]\sigma = \sqrt{{\sum^\:n}_{i=1}{\dfrac{(x_i-\overline{x})^2}{n}}\\[/tex]
here n = 4 and x assumes 9, 11, 12 and 16 and mean is 12, thus putting values in the given formula,
[tex]\sigma = \sqrt{\dfrac{[(9-12)^2 + (11-12)^2 + (12-12)^2 + (16-12)^2]}{4}}\\\sigma = \sqrt{\dfrac{[3^2 + 1^2 + 4^2]}{4}}\\\sigma = \sqrt{\dfrac{26}{4}}\\\sigma = \sqrt{6.5}\\\sigma = 2.549..\\\sigma \approx 2.55[/tex]
Thus, standard deviation of given data set rounded to the hundredth place is 2.55
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