he variance of first 49 natural numbers is-
Answers
Given:
no of terms n = 49
To find:
variance σ =?
Step-by-step explanation:
- The term variance is outlined as a statistical mensuration of the spread between the numbers in an information set.
- Additionally, variance measures, however, way every variety in the set is from the mean and therefore from each alternative variety within the set.
- Variance is also denoted by this image : .
- Mathematically, it is expressed as :
where :
σ = variance
n= number of terms
x= total sum of terms
= average mean of terms
- Here n = 49
- The summation of the first 49 natural numbers is 1225.
i.e. x = 1225
- The average mean of the first 49 natural numbers is
- Put given values in the above equation
σ = 171.42
Hence the variance of the first 49 natural numbers is 171.42.
Given : first 49 natural numbers
To Find : Variance of first 49 natural numbers
Solution:
Variance of first n natural numbers = (n + 1)(n - 1) /12
n = 49
Variance = (49 + 1) (49 - 1) /12
= 50 * 48 / 12
= 50 * 4
= 200
Variance = 200
Variance of first n natural numbers = (n + 1)(n - 1) /12 can be found using
Variance = ( ∑n² ) / n - ((∑n) / n)²
= n(n + 1)(2n +1)/6n - (n (n + 1) /2n)²
(n + 1)(n - 1) /12
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