Problem

Given a dataset of {3, 5, 2, 8, 9}, calculate the standard deviation.

Answer

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Answer

Step 4: Take the square root of the mean of these squared differences. \\ \( \sqrt{7.44} \)

Steps

Step 1 ：Step 1: Calculate the mean (average) of the dataset. \\ \( \frac{3+5+2+8+9}{5} = \frac{27}{5} = 5.4 \)

Step 2 ：Step 2: Subtract the mean from each data point and square the result. \\ \[ \begin{align*} (3-5.4)^2 &= 5.76 \\ (5-5.4)^2 &= 0.16 \\ (2-5.4)^2 &= 11.56 \\ (8-5.4)^2 &= 6.76 \\ (9-5.4)^2 &= 12.96 \end{align*} \]

Step 3 ：Step 3: Calculate the mean of these squared differences. \\ \( \frac{5.76 + 0.16 + 11.56 + 6.76 + 12.96}{5} = \frac{37.2}{5} = 7.44 \)

Step 4 ：Step 4: Take the square root of the mean of these squared differences. \\ \( \sqrt{7.44} \)

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