###
**The mean of $1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2}, 7^{2}$ is.
**

A. 10
B. 20
C. 30
D. 40
**Answer: Option B**

## Show Answer

Solution(By Apex Team)

$\begin{aligned}&1^2+2^2+3^2+\ldots.+n^2=\frac{n(n+1)(2n+1)}{6}\\
&\therefore1^2+2^2+3^2+\ldots.+7^2=\left(\frac{7\times8\times15}{6}\right)=140\\
&\text{ So, required average }\\
&=\left(\frac{140}{7}\right)\\
&=20\end{aligned}$

## Related Questions On Average

### Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average19 people went to a hotel for combine dinner party 13 by 8 runs. His new average is:

A. 20B. 21

C. 28

D. 32

### Find the average of all the numbers between 6 and 34 which are divisible by 5.

A. 18B. 20

C. 24

D. 30

### In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?

A. 10 yearsB. 10.5 years

C. 11 years

D. 12 years

### If the arithmetic mean of 0, 5, 4, 3 is a, that of -1, 0, 1, 5, 4, 3 is b and that of 5, 4, 3 is c, then the relation between a, b, and c is.

A. a = b = cB. a : b : c = 3 : 2 : 4

C. 4a = 5b = c

D. a + b + c = 12