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SAT Math: Data Analysis

Averages

The average (arithmetic mean) of the weights of 26 stones is p pounds.  In terms of p, what is the total weight of the stones, in pounds?  

A. 26 + p
B. p - 26 
C. p / 26
D. 26 / p
E. 26p

Knowsys Method

Read the problem carefully.  Be sure to keep the numbers in this problem straight so that you do not make any careless mistakes in your work. 

Identify the bottom line.   total weight  of the 26 stones = ?

Assess your options.  You could pick a number for p and then use it to find the total weight or you could leave p as a variable.  Either way, you need to use the "average formula," which you should definitely memorize.  Every time you see the word "average" on the exam, you should immediately think:  "average = the sum divided by the number."  Let's use that formula to solve this problem quickly and easily. 

The Average Formula

average formula.gif

Attack the problem.  

We are looking for the "total weight," which is the same thing as the SUM.  So, let's rearrange to get:

average * number = sum 

In this particular problem we know the average = p and the number = 26.  Let's just plug in to get:  

p(26) = sum

  26p = sum 

Loop back.  Verify that you solved for the bottom line.

The correct answer is E.

Level = Medium  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

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