Question:
If \( \sum_{i=1}^{10} (x_i - 3) = 7 \) and \( \sum_{i=1}^{10} (x_i - 3)^2 = 27 \), then the standard deviation of the 10 items is
If \( \sum_{i=1}^{10} (x_i - 3) = 7 \) and \( \sum_{i=1}^{10} (x_i - 3)^2 = 27 \), then the standard deviation of the 10 items is
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Shifted data formulas reduce heavy calculations in statistics.
Updated On: Apr 22, 2026
- 2.547
- 1.87
- 14.86
- 1.486
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The Correct Option is D
Solution and Explanation
Concept:
\[
\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}}
\]
Step 1: Mean.
\[ \sum x_i = 7 + 30 = 37 \Rightarrow \bar{x} = \frac{37}{10} \]
Step 2: Variance formula.
\[ \sigma^2 = \frac{27}{10} - \left(\frac{7}{10}\right)^2 = 2.7 - 0.49 = 2.21 \]
Step 3: Standard deviation.
\[ \sigma = \sqrt{2.21} \approx 1.486 \]
Step 1: Mean.
\[ \sum x_i = 7 + 30 = 37 \Rightarrow \bar{x} = \frac{37}{10} \]
Step 2: Variance formula.
\[ \sigma^2 = \frac{27}{10} - \left(\frac{7}{10}\right)^2 = 2.7 - 0.49 = 2.21 \]
Step 3: Standard deviation.
\[ \sigma = \sqrt{2.21} \approx 1.486 \]
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