If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $\frac{20}{3},$  respectively, then the value of $\left|a-b\right|$  is equal to

a, b, c, d, e be 5 unknown

n = 7, mean = 8, variance = 16

sum of observations = 7 × 8 = 56

mean of 5 remaining observation = $\frac{56-8-6}{25}=\frac{42}{5}$

$16=\frac{\sum x_i^2}{7}-64$

$\sum x_i^2=560$

$\begin{array}{l}{a}^2+b^2+c^2+d^2+e^2=460\\ =460-{\left(\frac{42}{5}\right)}^2\end{array}$

$=\frac{536}{25}$                                               &nbs