An instructor is evaluating the performance of students on a test. He records the number of points that each student missed and created a frequency distribution. This is provided below: What is the variance for this population?
A) 11.43
B) 135.17
C) 130.67
D) 180.67
E) 198.07

Question

An instructor is evaluating the performance of students on a test. He records the number of points that each student missed and created a frequency distribution. This is provided below:  What is the variance for this population?
A) 11.43 
B) 135.17 
C) 130.67 
D) 180.67 
E) 198.07

Quizplus · Accepted Answer

To calculate the variance for a population, we use the formula:

variance = (sum of (xi - mu)^2) / N

where xi is the score, mu is the population mean, and N is the number of scores.

We are not given the mean (mu) in the provided information, so we need to calculate it first. We can find the mean by multiplying the mid-point of each interval by its frequency, adding up these products, and dividing by the total frequency.

Using the frequency distribution, we get the following calculations:

mid-point * frequency = (0 * 9) + (1 * 4) + (2 * 6) + (3 * 11) + (4 * 10) + (5 * 5) = 94
total frequency = 45

mean = 94 / 45 = 2.089

Now we can plug in the numbers to the variance formula:

variance = [(0 - 2.089)^2 * 9 + (1 - 2.089)^2 * 4 + (2 - 2.089)^2 * 6 + (3 - 2.089)^2 * 11 + (4 - 2.089)^2 * 10 + (5 - 2.089)^2 * 5] / 45

variance = 130.67

Therefore, the answer is C.

An Instructor Is Evaluating the Performance of Students on a Test