Question

The variance of 2, 4, 6, 8, 10 is
A) 8
B) $\sqrt 8 $
C) 9
D) None of these

Answer 1

Hint: In this question, we will first find the mean of the data given and then find the sum of the squared distance of each term from mean. Lastly, divide the result from N (number of terms).

Complete step-by-step answer:
Given series is 2, 4, 6, 8, 10
Number of terms (N) = 5
 Since we know that:
The variance (σ2) , is defined as the sum of the squared distances of each term in the distribution from the mean (μ), divided by the number of terms in the distribution (N).
First we will find the mean as follows:
Mean = $\dfrac{{Sum.ofObservations}}{{No.ofObservations}}$
     = $\dfrac{{2 + 4 + 6 + 8 + 10}}{5}$
     = $\dfrac{{30}}{5}$
     = $6$
Now, we will find the variance denoted by σ2
To find the variance, we will find the square of each term subtracted from mean, divided by the total number of terms.
Variance = $\dfrac{{{{(2 - 6)}^2} + {{(4 - 6)}^2} + {{(6 - 6)}^2} + {{(8 - 6)}^2} + {{(10 - 6)}^2}}}{5}$
       = $\dfrac{{16 + 4 + 0 + 16 + 4}}{5}$
       = $\dfrac{{40}}{5}$
     = $8$

Option A is the correct answer.

Note: In this question, we have to find the variance of the given data, but for that we have to first find the mean of the data using the formula Mean = $\dfrac{{Sum.ofObservations}}{{No.ofObservations}}$ after that we will find the variance by subtracting the mean from the given data and squared them.
While finding variance, we should note that no negative number will be there as we are taking the square of the numbers.