Question

Given $\sum _{i=1}^9$(x_i - 5) = 9 $\Rightarrow$$\Sigma$x_i = 54 ..... (1)
Also,$\sum _{i=1}^9$(x_i - 5)² = 45
$\Rightarrow$$\Sigma$x_i² - 10.$\Sigma$x_i + 9(25) = 45
$\Rightarrow$$\Sigma$x_i² 360    (using (1))     ..... (2)
As, variance = $\frac{\Sigma {x_i}^2}{9}-{\left(\frac{\Sigma {x_i}^{}}{9}\right)}^2$
$=\frac{360}{9}-{\left(\frac{54}{9}\right)}^2$
= 40 - 36
= 4
Hence standard deviation is 2 (As standared
deviation = $\sqrt{var iance}$