The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is

Let 20 observation be x₁ , x₂ ,....., x₂₀ <br><br>Mean = <span style="display: inline-block;vertical-align: middle;"> <div style="text-align: center;border-bottom: 1px solid black;">x₁ + x₂ +, .....+ x₂₀</div> <div style="text-align: center;">20</div> </span> = 10 <br><br>$\Rightarrow$ x₁ + x₂ +, .....+ x₂₀ = 200 <br><br>Variance = $${{\sum\limits_{i = 1}^{i = n} {x_i^2} } \over n} - {\left( {\overline x } \right)^2}$$ <br><br>$\Rightarrow$ 4 = ${{x_1^2 + x_2^2 + ... + x_{20}^2} \over {20}}$ - 10² <br><br>$\Rightarrow$ ${x_1^2 + x_2^2 + ... + x_{20}^2}$ = 2080 <br><br>Also x₁ + x₂ +, .....+ x₂₀ - 9 + 11 = 202 <br><br>new variance will be <br><br>= ${{x_1^2 + x_2^2 + ... + x_{20}^2 - 81 + 121} \over {20}}$ - ${\left( {{{202} \over {20}}} \right)^2}$ <br><br>= 3.99