Question

The mean of 1², 2², 3², 4², ......19², 20² is
1. 143·5 
2. 134·5
3. 154·4
4. None of the above

Answer 1

Correct Answer - Option 1 : 143·5 

Formula used

Sum of squares of first 'n' natural numbers = [n(n + 1)(2n + 1)]/6

Mean = Sum of observations/Number of observations

Calculation

Sum of terms = 1² + 22 + 32 + 42......192 + 202 

⇒ n = 20

Sum = [20(20 + 1)(2 × 20 + 1)]/6

⇒ [20 × 21 × 41]/6

⇒ 17220/6 = 2870

Mean = Sum of observations/Number of observations

⇒ Mean = 2870/20 = 143.5

∴ Mean is 143.5