The mean of the squares of first ten natural numbers is:

Correct option is A

Given:

First ten natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Formula Used :

Mean = $$\frac{\text{(Sum of observations) }}{\text{ (Number of observations)}}$$​​

Sum of the squares of the first n natural numbers:$$\frac{n(n + 1)(2n + 1) } 6$$​​

Solution:

Using the formula for the sum of the squares of the first n natural numbers, where n = 10:

Sum of squares = $$\frac{10(10 + 1)(2 \times 10 + 1) } 6$$​​

Sum of squares =$$\frac{ 10(11)(21) } 6$$​​

Sum of squares = $$\frac{2310 } 6$$​​

Sum of squares = 385

Mean $$=\frac{ 385}{10}=\frac{77}2$$​​