Question

The average of the squares of first 7 natural numbers is

Answer 1

The average of the squares of first 7 natural numbers is 20

Given :

The first 7 natural numbers

To find :

The average of the squares of first 7 natural numbers

Solution :

Step 1 of 3 :

Write down first 7 natural numbers

The first 7 natural numbers are 1 , 2 , 3 , 4 , 5 , 6 , 7

Step 2 of 3 :

Calculate sum of the squares of first 7 natural numbers

The squares of first 7 natural numbers are 1, 4, 9, 16, 25, 36, 49 respectively

Number of observations = 7

Sum of the squares of first 7 natural numbers

= 1 + 4 + 9 + 16 + 25 + 36 + 49

= 140

Step 3 of 3 :

Calculate the average

The average of the squares of first 7 natural numbers

$\displaystyle \sf{ = \frac{Sum \: of \: the \: observations}{Number \: of \: observations} }$

$\displaystyle \sf{ = \frac{140}{8} }$

$\displaystyle \sf{ = 20}$

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Answer 2

Step-by-step explanation:

We know that,

$\boxed{\sf Avarage= \dfrac{Sum \: of \: observations}{Number \: of \: observations}}$

$\sf\longmapsto \dfrac{(1)^2+(2)^2+(3)^2+(4)^2+(5)^2+(6)^2+(7)^2}{7}$

$\sf \longmapsto \dfrac{1+4+9+16+25+36+49}{7}$

$\sf \longmapsto \dfrac{140}{7}$

$\sf \longmapsto 20$