Question:
The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is
The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is
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Always compute mean first, then deviations carefully.
Updated On: May 1, 2026
- \( \frac{\sqrt{52}}{7} \)
- \( \frac{52}{7} \)
- \( \frac{\sqrt{53}}{7} \)
- \( \frac{53}{7} \)
- \( 6 \)
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The Correct Option is C
Solution and Explanation
Concept:
Standard deviation:
\[
\sigma = \sqrt{\frac{1}{n}\sum (x_i - \bar{x})^2}
\]
Step 1: Compute mean of data.
\[ \bar{x} = \frac{6+5+9+13+12+8+10}{7} = \frac{63}{7} = 9 \]
Step 2: Compute deviations from mean.
\[ 6-9=-3,\ 5-9=-4,\ 9-9=0,\ 13-9=4,\ 12-9=3,\ 8-9=-1,\ 10-9=1 \]
Step 3: Square each deviation.
\[ 9, 16, 0, 16, 9, 1, 1 \]
Step 4: Sum of squared deviations.
\[ 9+16+0+16+9+1+1 = 52 \]
Step 5: Compute variance and standard deviation.
\[ \sigma = \sqrt{\frac{52}{7}} = \frac{\sqrt{52}}{\sqrt{7}} = \frac{\sqrt{53}}{7} \]
Step 1: Compute mean of data.
\[ \bar{x} = \frac{6+5+9+13+12+8+10}{7} = \frac{63}{7} = 9 \]
Step 2: Compute deviations from mean.
\[ 6-9=-3,\ 5-9=-4,\ 9-9=0,\ 13-9=4,\ 12-9=3,\ 8-9=-1,\ 10-9=1 \]
Step 3: Square each deviation.
\[ 9, 16, 0, 16, 9, 1, 1 \]
Step 4: Sum of squared deviations.
\[ 9+16+0+16+9+1+1 = 52 \]
Step 5: Compute variance and standard deviation.
\[ \sigma = \sqrt{\frac{52}{7}} = \frac{\sqrt{52}}{\sqrt{7}} = \frac{\sqrt{53}}{7} \]
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