Measures of Center

Question

Calculate the GPA of a student with the following grades: A (13 hours), C (21 hours), D (17 hours). Note that an A is equivalent to a 4.0, a B is equivalent to a 3.0, a C is equivalent to a 2.0, a D is equivalent to a 1.0, and an F is equivalent to a 0. Round your answer two decimal places

Answer 1

Hi Seth,

This is an example of a statistics discrete distribution and is also called a weighted mean. To find it, you multiply the percent of total hours that each letter grade makes up times the value of that letter grade.

First, compute the total hours in the distribution, 13+21+17=51 total hours.

Then, divide each letter grade's hours by the total hours to find that letter grade's percentage: for an "A", 13/51=0.2549, "C" 21/51=0.4118, and "D" 17/51=0.3333. (To double-check your math thus far, you could add up all of these percentages and they must add up to exactly 1 (allowing for slight rounding))

Next, multiply each of these percentages by the GPA value of its letter and sum those up for the final answer:

0.2549(4) + 0.4118(2) + 0.3333(1) = 1.0196 + 0.8236 + 0.3333 = 2.1765, or rounded to 2.18.

Hope that helps!