A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is:
A)6.07.
B)36.82.
C)5.16.
D)22.86.

Question

Quizplus · Accepted Answer

To find the population variance, we first need to find the population mean, which is (7+11+12+18+20+22+25)/7 = 15. 
Then, we calculate the sum of the squared differences between each data point and the mean: (7-15)^2 + (11-15)^2 + (12-15)^2 + (18-15)^2 + (20-15)^2 + (22-15)^2 + (25-15)^2 = 668. 
Finally, we divide by the total number of data points to get the population variance: 668/7 = 95.43/7 = 13.63. 
So, the closest choice is B, which is 36.82 (rounded to two decimal places). Note that this is the sample variance equation with n replaced by N, the population size. However, in practice, we usually use the sample variance formula with n-1 in the denominator when we only have a sample of the population, rather than the entire population.

A Population Consists of the Following Data: 7, 11, 12