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SAT Math: Data Analysis

Descriptive Statistics

Class A has 20 students and Class B has 28 students.  Both classes took the same test.  If Class A averaged an 83 and Class B averaged a 73, what is the best estimate of the average for all of the students together?

A.  75

B.  76

C.  77

D.  78

E.  79

 

Knowsys Method

Read the question carefully.  Notice that the two classes do NOT have the same number of students.  When two groups have unequal numbers, you cannot simply average the group averages.  Think about it; the class that has more students has to count more towards the average than the class that has fewer students in order for each student to be given the same consideration.  When you average two unequal groups, it is called a weighted average.

Identify the bottom line.  You need the total average of all of the students.  Make a note: Avg = ?

Assess your options.  You could try to estimate the answer, but there is no reason to be imprecise when the answer choices are so close together and you can find the exact average with a single formula.

Attack the problem.  Use the weighted average formula from your Knowsys handbook.  Class A is group 1 and Class B is group 2.

(Even if you don't know the weighted average formula, you can arrive at it logically.  Let's say you wanted to pick a number to represent each student in Class A.  If the class average is 83, you can just pick the number 83 to represent what each student scored.  You could pick a 73 to represent what each of the students in Class B scored.  Then you need to find the total score for both classes.  The easiest way to do that would be to multiply the score of the students in each class by the number of students in the class.  Finally, you would add the totals of the two classes and divide that total score by the total number of students to get your total average.  If this explanation seems unclear, take a look at the formula below and think about why it works.)

weighted avg.PNG

Loop back.  The exact answer is not among your answer choices, but if you round your answer, C is the best choice.

 

The correct answer is (C).

This is a hard question.

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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