# What is the mean of the square of first 11 natural numbers?

## What is the mean of the square of first 11 natural numbers?

The mean of the square of first 11 natural numbers is 46.

What is the mean of first n natural number?

Sum of first ′n′ natural numbers is given by 2n(n+1) ∴ Mean of these ′n′ natural numbers will be n2n(n+1)=2n+1.

How do you find the squares of a first n natural number?

Natural numbers include whole numbers in them except the number 0. If we need to calculate the sum of squares of n consecutive natural numbers, the formula is Σn2 = n×(n+1)×(2n+1)6 n × ( n + 1 ) × ( 2 n + 1 ) 6 . It is easy to apply the formula when the value of n is known.

### What is the sum of squares of first n natural numbers?

Sum of Squares of First n Odd Numbers

Sum of: Formula
Squares of three numbers x2 + y2+z2 = (x+y+z)2-2xy-2yz-2xz
Squares of first ‘n’ natural numbers Σn2 = [n(n+1)(2n+1)]/6
Squares of first even natural numbers Σ(2n)2 = [2n(n+1)(2n+1)]/3
Squares of first odd natural numbers Σ(2n-1)2 =[n(2n+1)(2n-1)]/3

What is the mean of the squares of the first 10 natural numbers?

38.5
Therefore, the mean of the squares of the first 10 natural numbers is 38.5.

What is the average of first n natural numbers?

Prerequisite : Sum of first n natural numbers. As discussed in previous post, sum of n natural number n(n+1)/2, we find the Average of n natural number so divide by n is n(n+1)/2*n = (n+1)/2.

#### Is it right to say that the mean of first n natural numbers is N 1 2 justify?

Median means middlemost number of the data set. Consider first n , natural numbers, that is from 1,2,3,4,………..n. So, we can’t say Surely that median of first n natural numbers in data set is .

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What is the square of n natural numbers?

Sum of Squares Formulas

In Statistics Sum of Squares: = Σ(xi + x̄)2
In Algebra Sum of Squares of Two Values: = a2 + b2 = (a + b)2 − 2ab
For “n” Terms Sum of Squares Formula for “n” numbers = 12 + 22 + 32 ……. n2 = n(n+1)(2n+1)/6

How do you find the sum of n squares?

What is the sum of squares formula in statistics, algebra, and in ‘n’ terms?

1. In Statistics: Sum of Squares = Σ(xi + x̄)2
2. In Algebra: Sum of Squares of Two Values = a2 + b2 = (a + b)2 − 2ab.
3. For “n” Terms: Sum of Squares Formula for “n” numbers = 12 + 22 + 32 ……. n2 = n(n+1)(2n+1)/6.

## How do you find the sum of n?

Usually, we consider arithmetic progression, while calculating the sum of n number of terms….Sum of N Terms of AP And Arithmetic Progression.

Sum of n terms in AP n/2[2a + (n – 1)d]
Sum of square of ‘n’ natural numbers [n(n+1)(2n+1)]/6
Sum of Cube of ‘n’ natural numbers [n(n+1)/2]2