The Grades In Mathematics Of The Students In Section A Are As Follows: 80, 75, 60, 95, 100. What Is The Populaton Mvariance Of Their Group?

The grades in mathematics of the students in section A are as follows: 80, 75, 60, 95, 100. What is the populaton mvariance of their group?

 

Answer:

The population variance is 206.

Step-by-step explanation:

Steps in solving for the population variance:

1) Find the mean by adding the values of (the grades in Math), then divide the sum by number of observations.

Total Values (x):

∑x = (60 + 75 + 80 + 95 + 100)

∑x = 410

Population Mean:

μ = ∑x/N    Where N = 5

μ =410/5

μ = 82

2) Subtract the mean from each x ⇒  (x - μ):

60 – 82 = - 22

75 – 82 = -7

80 – 82 = -2

95 – 82 = 13

95 – 82 = 18

3.) Square each difference between x and mean ⇒   (x - μ)²:

(-22)2 = 484

(-7)2 = 49

(-2)2 = 4

(13)2 = 169

(18)2 = 324

4.) Add the results in #3:

∑(x - μ)² = (484 + 49 + 4 + 169 + 324)

∑(x - μ)² = 1,030

5.) Solve of the population variance (σ) by dividing the sum in #4 by the number of observations (N):

Population Variance:

σ² = ∑(x - μ)²  / N

σ² = 1,030/5

σ² = 206

Please click the image below to view the Table.