The calculation of averages is covered on many standardized examinations.
Calculating averages is an important mathematical skill, especially for teachers, who will need to calculate the averages for students’ scores.
You will see different variations of problems involving averages on your test.
The first type of math problem you might see will be on the basic computation of averages.
Basic Computation of Averages
(1) A group of people are collecting money for a fund-raising event. Person A has collected $150; Person B has collected $175, and Person C has collected $125.
What is the average amount of collection per person for this group?
A. $125
B. $140
C. $150
D. $160
E. $175
Tip: Remember that basic averages are calculated by taking the total data set for a group and dividing this total by the number of people in the group.
STEP 1: Add up the total for the data set.
Person A: $150
Person B: $175
Person C: $125
Total = $150 + $175 + $125 = $450
STEP 2: Divide the total by the number of people or items in the group.
Here we have three people.
So, we divide $450 by 3 in order to get the average.
Average = $450 ÷ 3 = $150
So, the correct answer is C.
Advanced Math Problems on Averages
(2) A class of 50 students took an exam. The 30 female students in the class had an average score of 85, while the 20 male students in the class had an average of 90. What is the average test score for all 50 students in the class?
A. 85
B. 85.5
C. 86
D. 87
E. 88
Tip: You still need to find the total for the data set, but for problems like this one, you will need to multiply, as well as add.
STEP 1: Calculate the total for the data set.
Total Points for the Female Students: 30 × 85 = 2,550
Total Points for the Male Students: 20 × 90 = 1,800
Total points for the Class: 2,550 + 1,800 = 4,350
STEP 2: Divide the total by the number of people or items in the group.
Here we have 50 students: 30 girls and 20 boys.
So, we divide 4,350 by 50 in order to get the average.
Average = 4,350 ÷ 50 = 87
So, the correct answer is D.
Correcting an Erroneous Average Calculation
(3) Tom wanted to find the average of the four tests he has taken for class so far this term. When doing his original calculation, he erroneously divided his total points from the four tests by 5, which gave him an erroneous average of 76. What is the correct average of his four tests?
A. 83
B. 85
C. 88
D. 93
E. 95
STEP 1: Find the total points by multiplying the erroneous average by 5
76 × 5 = 380
STEP 2: Divide the total points from step 1 by the correct number of exams.
380 ÷ 4 = 95
So, the correct answer is E.