The largest deviation for this case is from the dataset C so then the answer would be Data set C.
How is standard deviation calculated?
Suppose that the considered data set is
Then, its standard deviation is the positive square root of the variance of this data set.
A variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.
Thus, we get:
[tex]\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2[/tex]
And for this case we have the deviations for each dataset are given by:
[tex]s_a = 5.21\\\\s_b =4.88\\\\s_c = 6.06\\\\s_d = 3.39\\[/tex]
We need to remember that the deviation is a measure of dispersion.
For this case, if the deviation is larger then we have more spread out the distribution of interest.
And largest deviation for this case is from the dataset C so then the answer would be:
Thus, the correct answer is D. Data set C.
Learn more about standard deviation;
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