Suppose a class has 7 students. The average marks of these students...

Applying the formula of variance we get,

$20 = \dfrac{{∑}_{i = 1}^{7}{\left|{x}_{i} - 62\right|}^{2}}{7}$

$⇒ {\left|{x}_{1} - 62\right|}^{2} + {\left|{x}_{2} - 62\right|}^{2} + \ldots . + {\left|{x}_{7} - 62\right|}^{2} = 140$

If ${x}_{1} = 49$ (taking the least possibility)

${\left|49 - 62\right|}^{2} = 169$

then,

${\left|{x}_{2} - 62\right|}^{2} + \ldots . + {\left|{x}_{7} - 62\right|}^{2} = 140 - 169 = - 29$ Negative Number which is not possible, therefore, no student can fail.