Question:
If mean and standard deviation of 5 observations \(x_1, x_2, x_3, x_4, x_5\) are 10 and 3, respectively, then the variance of 6 observations \(x_1, x_2, \ldots, x_5\) and \(-50\) is equal to
If mean and standard deviation of 5 observations \(x_1, x_2, x_3, x_4, x_5\) are 10 and 3, respectively, then the variance of 6 observations \(x_1, x_2, \ldots, x_5\) and \(-50\) is equal to
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Find \(\sum x_i\) and \(\sum x_i^2\) from the given mean and SD, add the new observation, and recompute the variance.
Updated On: Nov 5, 2026
- 582.5
- 507.5
- 586.5
- 509.5
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The Correct Option is B
Solution and Explanation
\(\sum x_i = 5\times10 = 50\).
Variance \(= 9 = \frac{\sum x_i^2}{5} - 10^2 \Rightarrow \sum x_i^2 = 5\times109 = 545\).
With the sixth observation \(-50\): sum \(= 50 - 50 = 0\), so the new mean is 0; \(\sum x^2 = 545 + 2500 = 3045\).
New variance \(= \frac{3045}{6} - 0^2 = 507.5\).
Answer: (2) 507.5
Variance \(= 9 = \frac{\sum x_i^2}{5} - 10^2 \Rightarrow \sum x_i^2 = 5\times109 = 545\).
With the sixth observation \(-50\): sum \(= 50 - 50 = 0\), so the new mean is 0; \(\sum x^2 = 545 + 2500 = 3045\).
New variance \(= \frac{3045}{6} - 0^2 = 507.5\).
Answer: (2) 507.5
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