Question

Suppose your statistics instructor gave six examinations during the semester. You received the following exam scores (percent correct): 79, 64, 84, 82, 92, and 77. To compute your final course grade, the instructor decided to randomly select two exam scores, compute their mean, and use this score to determine your final course grade.
a. Compute the population mean. This is your average grade based on all of your grades. (Round your answer to 2 decimal places.)
b. Compute the population standard deviation. (Round your answer to 2 decimal places.)

Answer 1

Answer: a) the population mean is 79.67

b) the population standard deviation is 6.20

Explanation:

a) to calculate the population mean, add all the values together, and then divide by the number of values added: (79+64+84+82+92+77)/6 = 478/6 = 79.67

b) to calculate to population standard deviation, take each value and subtract the mean, square each answer and add them all together, then divide the answer by the number of values added - 1:

$(79-79.67)^{2} + (64 -79.67)^{2} + (84-79.67)^{2} + (82-79.67)^{2} + (92-79.67)^{2} + (77-79.67)^{2} = 429.33$

429.33/(6-1) = 85.87

The standard deviation will be the difference between this value and the mean:

85.87 - 79.67 = 6.20