The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is

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Payal Gupta | Contributor-Level 10

2 months ago

$\bar{x} = \frac{\sum_{i = 1}^{10} x_{i}}{10} = 15 \frac{\sum_{i = 1}^{10} {x_{i}}^{2}}{10} - {(\bar{x})}^{2} = 15$

$\Rightarrow Σ x_{i} = 150 Σ {x_{i}}^{2} = 2400$

Actual mean $\bar{x} = \frac{Σ x_{i} + 15 - 25}{10} = \frac{140}{10} = 14$

Actual variance = $\frac{Σ {x_{i}}^{2} + 1 5^{2} - 2 5^{2}}{10} - {(14)}^{2}$

$= \frac{2400 - 400}{10} - 196$

$\begin{array}{l} σ^{2} = 4 \\ σ = 2 \end{array}$

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The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is

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