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

Table of Contents

## 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 .

**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?

- 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?

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] |
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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 |