Calculate the population variance of these numbers to the nearest hundredth. 5 0 -7 14 5 2 7 2 2 15 11 -9

Question

Calculate the population variance of these numbers to the nearest hundredth.

5
0
-7
14
5
2
7
2
2
15
11
-9

Answer 1

To calculate the variance, I set up the following table,

 

 X        X-μ             (X-μ)² 

---      -----             ------

  5      -0.41666      0.1736111

  0      -5.41666    29.3402777

-7      -12.4166    154.173609

14        8.5833      73.6736111

 5       -0.41666      0.1736111

 2       -3.41666     11.6736111

 7        1.58333       2.5069444

 2       -3.41666     11.674111

 2       -3.41666     11.674111

15       9.58333      91.8402777

11       5.58333      31.1736111

-9     -14.41666     207.840276

---                       -------------- 

65                        622.917662     Variance = 622.917662/12 = 51.91

 

μ = 65/12 = 5.416666

 

The steps are:

1) sum the data and divide by the total to get the mean (μ)

2) Subtract the mean from each data point

3) Square the result of step 2

4) sum the results of step 3

5) divide the sum in step 4 by the number of data points for the population variance.