A mean is an arithmetic average of a set of observations. The standard deviation for the data set is 6.1869. Thus, none of the options is correct.
A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
For the given data set 37, 42, 48, 51, 52, 53, 54, 54, 55; the mean can be written as,
Mean, μ = (37 + 42 + 48 + 51 + 52 + 53 + 54 + 54 + 55)/9
= 49.5556
Now, the value of the (x-μ) and (x-μ)² can be calculated as shown below. Using the value to calculate the standard deviation we will get,
[tex]\sigma = \sqrt{\dfrac{\sum(x-\mu)^2}{n-1}}[/tex]
[tex]=\sqrt{\dfrac{306.2222222}{9-1}}[/tex]
= √38.277775
= 6.1869
Hence, the standard deviation for the data set is 6.1869. Thus, none of the options is correct.
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