Given $${{\sum\limits_{i = 1}^{10} {{x_i}} } \over {10}} = 15$$ ..... (1)

$$ \Rightarrow \sum\limits_{i = 1}^{10} {{x_i} = 150} $$

and $${{\sum\limits_{i = 1}^{10} {x_i^2} } \over {10}} - {15^2} = 15$$

$$ \Rightarrow \sum\limits_{i = 1}^{10} {x_i^2 = 2400} $$

Replacing 25 by 15 we get

$$\sum\limits_{i = 1}^9 {{x_i} + 25 = 150} $$

$$ \Rightarrow \sum\limits_{i = 1}^9 {{x_i} = 125} $$

$$\therefore$$ Correct mean $$ = {{\sum\limits_{i = 1}^9 {{x_i} + 15} } \over {10}} = {{125 + 15} \over {10}} = 14$$

Similarly, $$\sum\limits_{i = 1}^2 {x_i^2 = 2400 - {{25}^2} = 1775} $$

$$\therefore$$ Correct variance $$ = {{\sum\limits_{i = 1}^9 {x_i^2 + {{15}^2}} } \over {10}} - {14^2}$$

$$ = {{1775 + 225} \over {10}} - {14^2} = 4$$

$$\therefore$$ Correct $$S.D = \sqrt 4 = 2$$.