SAT Math: Data Analysis

Descriptive Statistics

Given the set S = {5, 9, 49, 6, 3, 8, 9, 12, 4}, what is the difference between the range and the median of set S? 

A.   1

B.   8

C.  12

D.  37

E.  38


Knowsys Method

Read the question carefully.  This question will have multiple steps because it asks for the difference between the range and the median, both of which you must find.

Identify the bottom line.  Make a note on your paper to remind you to find the difference: diff = ?

Assess your options.  There is not really a way to work backwards from the answer choices, so you must use your understanding of the terms "range" and "median."

Attack the problem.  You know you will have to find the median eventually.  The median is the middle number in a series of numbers when they are arranged in numerical order.  Go ahead and arrange the series in numerical order because it will keep you from making mistakes as you find the range.

 {3, 4, 5, 6, 8, 9, 9, 12, 49}

Now start by finding the range.  The range of a set of numbers is the difference between the largest and the smallest terms.  Looking up at the numbers you reordered:

Range = 49 - 3 = 46

Now that you have the range, you also need the median.  The median is the middle number, so cover up one number in your set when it is arranged numerically.  The middle number is 8.

Your bottom line was to find the difference between the range and median, so subtract the smaller from the larger: 

46 - 8 = 38

 Loop back.  You completed every step of the problem by finding the bottom line, the difference between two other numbers.  Select your answer.


The correct answer is (E). 

This is a medium level question. 


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