The mean of 1², 2², 3², 4², 5², 6², 7² is -

Solution (By Examveda Team)

1² + 2² + 3² + . . . . . + n² = $$\frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$$
∴ 1² + 2² + 3² + . . . . . + 7² = $$\left( {\frac{{7 \times 8 \times 15}}{6}} \right)$$   = 140
So, required average
$$ = \left( {\frac{{140}}{7}} \right)$$
= 20