Average of squares of of first ten natural numbers is

English

Gujarati

Hindi

4.Average

medium

The average of the squares of of first ten natural numbers is

A

$35.5$

B

$36$

C

$37.5$

D

$38.5$

Solution

The sum of the squares of $n$ Natural numbers

$=\frac{n(n+1)(2 n+1)}{6}$

Average $=\frac{n(n+1)(2 n+1)}{6 \times n}=\frac{(n+1)(2 n+1)}{6}$

Average Square of $10$ Natural number

$=\frac{11 \times 21}{6}=\frac{77}{2}=38.5$

Standard 13

Quantitative Aptitude

Share

Similar Questions

The average of first $25$ numbers is $10$ and the average of the next $25$ numbers is $12 .$ The average of all $50$ numbers is

easy

The average age of $15$ students of a class is $15\, year.$ Oute of these, the average age of $5$ students is $14 \,year$ and that of the other $9$ students is $16\, year.$ The age of the $15^{th}$ students is? (in $year$)

medium

The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers ?

medium

The arithmetic mean of the following numbers is $1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7$

medium

In a set of prime and composite numbers, the composite numbers are twice the number of prime number and the average of all the numbers of the set is $9 .$ If the number of prime numbers and composite numbers are exchanged then the average of the set of numbers is increased by $2 .$ If during the exchange of the numbers the average of the prime numbers and composite numbers individually remained constant, then the ratio of the average of composite numbers to the average of prime numbers (initially) was

hard