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# 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

 B) 858.5

$$\large 1^2 + 2^2 + 3^2 + 4^2+ ..... +n^2 = \frac{n\left(n + 1\right)\left(2n + 1\right)}{6}$$

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

=42925

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

Part of solved Average questions and answers : >> Aptitude >> Average

 where are to come 2n+1 - shailesh,dixit

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