The mean of \( \large 1^2, 2^2,3^2,4^2,5^2,6^2 ....... 50^2 \) is

A) 850.5

B) 858.5

C) 854.5

D) 852.5

Correct answer:
B) 858.5

Description for Correct answer:
\( \large 1^2 + 2^2 + 3^2 + 4^2+ ..... +n^2 = \frac{n\left(n + 1\right)\left(2n + 1\right)}{6} \)

\( \large 1^2 + 2^2 + 3^2 + 4^2+ ..... +50^2 = \frac{50 \times 51 \times 101}{6}\)

=42925

Required average \( \large = \left( \frac{42925}{50} \right) = 858.5 \)


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