GRE Math : How to find range

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Example Questions

Example Question #135 : Data Analysis

Quantitative Comparison

A set of numbers, Set A, has a mean of 4 and a standard deviation of 2. Another set, Set B, has a mean of 100 and a standard deviation of 20.

Quantity A: dispersion of numbers in Set A

Quantity B: dispersion of numbers in Set B

Possible Answers:

Quantity A is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

The standard deviation tells us how much variation, or dispersion, there is on average between the numbers in a set and their mean. Therefore Quantity B is greater, because Set B has a larger standard deviation than Set A.

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Example Question #136 : Data Analysis

Find the range of the following set of numbers:

$\displaystyle 1, 2, 4, 5, 7, 9, 13, 15$

Possible Answers:

$\displaystyle 14$

$\displaystyle 6$

Cannot be determined.

$\displaystyle 7$

Correct answer:

$\displaystyle 14$

Explanation:

The range is the difference between the largest and smallest numbers of a set. The biggest number is 15 and the smallest is 1, so our range is 15 – 1 = 14.

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Example Question #581 : Gre Quantitative Reasoning

$\displaystyle G= [2, 4, 5, 5, 6, 6, 6, 10, 12]$

Quantity A:

The sum of the median and mode of Set G

Quantity B:

The range of Set G

Possible Answers:

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

The median is the middle value in a set of numbers, and the mode is the number that occurs.

In Column A, the median is 6 and the mode is 6, so the sum of the median and the mode of Set G is 12.

The range is the difference between the highest and lowest numbers of the set.

In Column B, the range is 12 – 2 = 10.

Column A is greater than Column B.

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Example Question #4 : Range

$\displaystyle SetQ=[2,5,3,7,8,7]$

Quantity A: The range of Set Q.

Quantity B: The median of Set Q.

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

The first step of this problem should be to reorder Set Q into numerical order:

$SetQ=[2,5,3,7,8,7]\rightarrow[2,3,5,7,7,8]$ $\displaystyle SetQ=[2,5,3,7,8,7]\rightarrow[2,3,5,7,7,8]$

The range of a set is the largest value minus the lowest value, so for this set, the range is 8-2=6 $\displaystyle 8-2=6$

The median of a set depends on whether or not there is an even or odd amount of numbers in the set. For a set $\displaystyle [x_1,x_2,...,x_n]$ with $\displaystyle n$ values:

Odd:

$Median=x_{\frac{n+1}{2}}$ $\displaystyle Median=x_{\frac{n+1}{2}}$

Even:

$Median=\frac{x_{\frac{n}{2}}+x_{\frac{n+2}{2}}}{2}$ $\displaystyle Median=\frac{x_{\frac{n}{2}}+x_{\frac{n+2}{2}}}{2}$

Since there is an even number of numbers in this set, the median is

$\frac{5+7}{2}=6$ $\displaystyle \frac{5+7}{2}=6$

The two quantities are equal.

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GRE Math : How to find range

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #135 : Data Analysis

Example Question #136 : Data Analysis

Example Question #581 : Gre Quantitative Reasoning

Example Question #4 : Range

All GRE Math Resources

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