Problem

Find the standard deviation for the group of data items.
\[
16,17,18,19,20
\]

Answer

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Answer

\(\boxed{\text{The standard deviation of the data set is approximately 1.41}}\)

Steps

Step 1 :Calculate the mean of the data set by adding all the numbers and dividing by the number of numbers: \(\frac{16 + 17 + 18 + 19 + 20}{5} = 18\)

Step 2 :Subtract the mean from each number and square the result to get the squared deviation of each number: \((16 - 18)^2 = 4\), \((17 - 18)^2 = 1\), \((18 - 18)^2 = 0\), \((19 - 18)^2 = 1\), \((20 - 18)^2 = 4\)

Step 3 :Find the mean of these squared deviations to get the variance: \(\frac{4 + 1 + 0 + 1 + 4}{5} = 2\)

Step 4 :Take the square root of the variance to get the standard deviation: \(\sqrt{2} \approx 1.41\)

Step 5 :\(\boxed{\text{The standard deviation of the data set is approximately 1.41}}\)

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