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 _____________.

<p>Given ${{\sum\limits_{i = 1}^{10} {{x_i}} } \over {10}} = 15$ ..... (1)</p> <p>$\Rightarrow \sum\limits_{i = 1}^{10} {{x_i} = 150}$</p> <p>and ${{\sum\limits_{i = 1}^{10} {x_i^2} } \over {10}} - {15^2} = 15$</p> <p>$\Rightarrow \sum\limits_{i = 1}^{10} {x_i^2 = 2400}$</p> <p>Replacing 25 by 15 we get</p> <p>$\sum\limits_{i = 1}^9 {{x_i} + 25 = 150}$</p> <p>$\Rightarrow \sum\limits_{i = 1}^9 {{x_i} = 125}$</p> <p>$\therefore$ Correct mean $$ = {{\sum\limits_{i = 1}^9 {{x_i} + 15} } \over {10}} = {{125 + 15} \over {10}} = 14$$</p> <p>Similarly, $\sum\limits_{i = 1}^2 {x_i^2 = 2400 - {{25}^2} = 1775}$</p> <p>$\therefore$ Correct variance $= {{\sum\limits_{i = 1}^9 {x_i^2 + {{15}^2}} } \over {10}} - {14^2}$</p> <p>$= {{1775 + 225} \over {10}} - {14^2} = 4$</p> <p>$\therefore$ Correct $S.D = \sqrt 4 = 2$.</p>