McGraw-Hill Education GRE 2019

Why? Because there will be 25 data points below this value and 25 data points

above this value.

A certain test was administered to 29 students. 6 students scored 60, 8

students scored 73, and 15 students scored 79. What was the median score for

the 29 students?

SOLUTION: The median is the 15th-largest (or smallest) score. The smallest

6 data points have a value of 60. The next 8 data points have a value of 73.

These two groups account for the first 14 data points. The next data point will

thus equal the median. That data point occurs in the last set. Since all the

data points in the last set are 79, the median is 79.

Standard Deviation

Standard deviation refers to how far from the mean the numbers in a set typically

fall. Two sets can have the same mean and the same number of items, but

completely different spreads from the mean. The concept of standard deviation is

employed to represent this spread. The greater the average spread of the data, the

greater the standard deviation. Look at the following three sets, all of which have

the same mean:

2, 2, 2, 2, 2

0, 1, 2, 3, 4

–2, 0, 2, 4, 6

In the first set, all the data points are equal, so there is no spread from the mean.

The standard deviation is thus zero. In the second set, the distance between

successive numbers is one, so the standard deviation is greater than in the first set.

In the third set, the distance between successive numbers is two, so the standard

deviation is even greater than in the second set.

You might be wondering what the standard deviations of the first and second

sets are. Fortunately, the GRE almost never tests the exact formula for standard

deviation. It does, however, expect you to understand the concept and to be able to

compare the standard deviation of different sets of numbers.

Which of the following sets has the greatest standard deviation?

A {4, 4, 4, 4, 4}

B {3, 4, 4, 4, 5}

C {3, 4, 4, 4, 8}

D {0, 2, 4, 4, 12}

E {1, 4, 4, 4, 7}

SOLUTION: Look at how the choices compare to A, which has a spread of zero.

The further the values in a set move away from 4, the greater the standard

deviation. The values in Choice D spread the most from 4. Thus the correct

answer is D.

CHAPTER 12 ■ FROM WORDS TO ALGEBRA 331

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