Weighted Averages

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

jslavi01: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Thu Jul 03, 2008 5:46 am; Location: Philadelphia

Weighted Averages

by jslavi01 » Thu Jul 24, 2008 11:10 am

From a practice test website...
How do you solve this? For the life of me I can't get it!!

2. At a certain high school, the respective weights for the following subjects are:
Mathematics 3, English 3, History 2, Science 2 and Art 1.
What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85?

A. 85.7
B. 87.8
C. 88.9
D. 89.4
E. 90.2

Quote

Source: Beat The GMAT — Problem Solving | Thu Jul 24, 2008 11:10 am

Travis_1234567890: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Mon Jul 07, 2008 3:38 pm; Location: Atlanta; Thanked: 6 times

by Travis_1234567890 » Thu Jul 24, 2008 12:17 pm

This is similar to figuring out your GPA

For each course…
Take the grade*weight = course total
Sum all course totals / Sum all weights = weighted average

Geometry
89 x 3 = 267
American Literature
92 x 3 = 276
American History
94 x 2 = 188
Biology
81 x 2 = 162
Sculpture
85 x 1 = 85

978 / 11 = 88.90909091 = 88.9 = C

Quote

Travis_1234567890: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Mon Jul 07, 2008 3:38 pm; Location: Atlanta; Thanked: 6 times

by Travis_1234567890 » Thu Jul 24, 2008 12:18 pm

This is similar to figuring out your GPA

For each course…
Take the grade*weight = course total
Sum all course totals / Sum all weights = weighted average

Geometry
89 x 3 = 267
American Literature
92 x 3 = 276
American History
94 x 2 = 188
Biology
81 x 2 = 162
Sculpture
85 x 1 = 85

978 / 11 = 88.90909091 = 88.9 = C

Quote

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Thu Jul 24, 2008 12:52 pm

Travis_1234567890 wrote:This is similar to figuring out your GPA

For each course…
Take the grade*weight = course total
Sum all course totals / Sum all weights = weighted average

Geometry
89 x 3 = 267
American Literature
92 x 3 = 276
American History
94 x 2 = 188
Biology
81 x 2 = 162
Sculpture
85 x 1 = 85

978 / 11 = 88.90909091 = 88.9 = C

Great solution!

Here's the general weighted average formula:

Weighted Average = %weight group1*avg group1 + %weight group2*avg group2 + .....

In this case, the total number of units is 3+3+2+2+1 = 11.

So, math is 3/11 of total, english is 3/11, history is 2/11, science is 2/11 and art is 2/11. If we apply the formula to this question, we'd get:

Weighted Average = (3/11)89 + (3/11)92 + (2/11)94 + (2/11)81 + (1/11)85

Note that because of the ugly numbers in this question, the formula involves a lot of annoying calculations. In this instance, Travis's approach is much quicker. In fact, Travis actually applied the formula, he just did things in a slightly different order. Travis did it as:

(3*89 + 3*92 + 2*94 + 2*81 + 1*85)/11

which is the exact same calculation.