Question

Sample mean and sample variance of the data 2, 7,3, 4, 1 are
Select one:
a. = 3.4, s2 = 6.52
O b. 8 = 2.5, s2 = 4.24
Oc. i = 3.4, s2 = 4.1
O d. ž= 2.6, s2 = 3.56​

Answer 1

Answer:

c) 3.4, s2= 4.1

Explanation:

Answer 2

The sample mean and sample variance of the data 2, 7, 3, 4, 1 are 3.4 and 4.1, respectively. (Option c)

Given:

Data: 2, 7, 3, 4, 1

To find:

The sample mean and sample variance

Solution:

We can find the solution by following a few simple steps-

We know that the mean can be calculated by dividing the sum of terms in the data by the number of terms.

The sum of all the terms= 2+7+3+4+1

=17

The number of terms=5

The mean of the data= The sum of all the terms/ the number of terms

=17/5

Mean= 3.4

The variance of all the terms= Sum of squares of the difference of terms and mean/ number of terms

The difference of terms and the mean is as follows-

2-3.4= -1.4

7-3.4= 3.6

3-3.4= -0.4

4-3.4= 0.6

1-3.4= -2.4

Now, on squaring the differences obtained, we get

(-1.4)²= 1.96

3.6²= 12.96

(-0.4)²= 0.16

0.6²= 0.36

(-2.4)²= 5.76

Add these terms to get the sum of squares

Sum of squares of difference of terms= 21.2

Variance= 21.2/5

=4.1

Therefore, the mean and variance of the data are 3.4 and 4.1, respectively.