Question:
The standard deviation of 9, 16, 23, 30, 37, 44, 51 is:
The standard deviation of 9, 16, 23, 30, 37, 44, 51 is:
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For any set of equally spaced numbers, the standard deviation is always proportional to the spacing \( d \). If you double the spacing, you double the standard deviation.
Updated On: May 6, 2026
- \( 7 \)
- \( 9 \)
- \( 12 \)
- \( 14 \)
- \( 16 \)
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The Correct Option is D
Solution and Explanation
Concept:
The given data is an arithmetic progression with a common difference \( d = 7 \). For any \( n \) terms in an A.P. with common difference \( d \), the variance \( \sigma^2 \) is given by:
\[ \sigma^2 = d^2 \left( \frac{n^2 - 1}{12} \right) \]
Step 1: Identify the parameters.
Data: 9, 16, 23, 30, 37, 44, 51. Number of terms \( n = 7 \). Common difference \( d = 16 - 9 = 7 \).
Step 2: Calculate the variance.
\[ \sigma^2 = 7^2 \left( \frac{7^2 - 1}{12} \right) \] \[ \sigma^2 = 49 \left( \frac{48}{12} \right) \] \[ \sigma^2 = 49 \times 4 = 196 \]
Step 3: Find the standard deviation.
Standard Deviation \( \sigma = \sqrt{\sigma^2} \): \[ \sigma = \sqrt{196} = 14 \]
Step 1: Identify the parameters.
Data: 9, 16, 23, 30, 37, 44, 51. Number of terms \( n = 7 \). Common difference \( d = 16 - 9 = 7 \).
Step 2: Calculate the variance.
\[ \sigma^2 = 7^2 \left( \frac{7^2 - 1}{12} \right) \] \[ \sigma^2 = 49 \left( \frac{48}{12} \right) \] \[ \sigma^2 = 49 \times 4 = 196 \]
Step 3: Find the standard deviation.
Standard Deviation \( \sigma = \sqrt{\sigma^2} \): \[ \sigma = \sqrt{196} = 14 \]
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