Question

What is the Average of squares of numbers from 1 to 21

Answer 1

the average of square s of numbers from 1to21 is 157.67

Answer 2

Step-by-step explanation:

Given:

The numbers from $1$ to $21.$

To find:

The Average of squares of numbers from $1$ to $21.$

Solution:

Here we want to find the average square of numbers from 1 to 21.

Therefore, Using the formula of the average of the square of natural numbers,

⇒ $1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$

Where $n=21,$

⇒  $1^2+2^2+3^2+...+21^2=\frac{21(21+1)(2(21)+1)}{6}$

⇒ $1^2+2^2+3^2+...+21^2=\frac{21(22)(43)}{6}$

⇒ $1^2+2^2+3^2+...+21^2=$ $\frac{19866}{6}=3311$

∴ Average $=\frac{3311}{21}=157.6666666$

Hence the answer is $157.67$ .

Answer:

The Average of squares of numbers from $1$ to $21$ is $157.67$ .