Question

The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class population. What is the value of the numerator of the calculation of the variance?

Answer 1

Variance is given by s^2 = [summation (x - mean)^2] / n.
mean = (90 + 75 + 72 + 88 + 85) / 5 = 82
Variance = [(90 - 82)^2 + (75 - 82)^2 + (72 - 82)^2 + (88 - 82)^2 + (85 - 82)] / 5
= [8^2 + (-7)^2 + (-10)^2 + 6^2 + 3^2] / 5
= (64 + 49 + 100 + 36 + 9] / 5
= 258 / 5
=258.

Answer 2

The value of the numerator of the calculation of the variance= 258

and Variance= 51.6

Explanation:

We know that in order to calculate the variance we need to follow following steps:

• First calculate mean.

• Then subtract each of the data points from means and square the difference quantity.

• Lastly calculate the mean of these squared quantity.

The data points are:

90, 75, 72, 88, 85

The mean of these data points are:

`Mean=(90+75+72+88+85)/(5)\\\\\\Mean=(410)/(5)\\\\\\Mean=82`

Now on finding the difference terms i.e.

90-82=8

75-82= -7

72-82= -10

88-82=6

and 85-82=3

The square of these difference term is:

8²=64

(-7)²=49

(-10)²=100

6²=36

and 3²=9

Hence, the mean of these squared quantity i.e. Variance is:

`Variance=(64+49+100+36+9)/(5)\\\\\\Variance=(258)/(5)\\\\\\Variance=51.6`