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? Variance: mc003-1.jpg -160 -6 16 258

Answer 1

The data given as a whole would be called ungrouped data. Now to get the variance, you will need the formula:

s^2=   Σ(x-mean)^2
                   n      

x = raw data
mean = average of all data
n = no. of observations
s^2 = variance

Now we do not have the mean yet, so you have to solve for it. All you need to do is add up all the data and divide it by the number of observations. 

Data: 90, 75, 72, 88, 85        n= 5  
Mean=Σx
            n
Mean = 90+75+72+88+85   = 410 = 82
                        5                        5

The mean is 82. Now we can make a table using this.

The firs column will be your raw data or x, the second column will be your mean and the third will be the difference between the raw data and the mean and the fourth column will be the difference raised to two. 

90-82 = 8
8^2 =64

75-82 = -7
-7^2 =49

72-82 = -10
-10^2=100

88-82=6
6^2 = 12

85-82=3
3^2=9

Now you have your results, you can now tabulate the data:

 x      mean         x-mean        (x-mean)^2     
90       82                8                      64                       
75       82               -7                      49
72       82              -10                    100
88       82                6                       36
85       82                3                       9

Now that you have a table, you will need the sum of (x-mean)^2 because the sigma sign Σ in statistics, means "the sum of."

64+49+100+36+9 = 258

This will be the answer to your question. The value of the numerator of the calculation will be 258.