GRE Subject Test: Math : Range & IQR

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Range & Iqr

What is the range of the set of numbers: \(\displaystyle 7,6,4,3,5,2,5,7,5,23,111,88,26\)?

Possible Answers:

\(\displaystyle 113\)

\(\displaystyle 109\)

\(\displaystyle 102\)

\(\displaystyle 115\)

Correct answer:

\(\displaystyle 109\)

Explanation:

Step 1: Arrange the numbers in the set from smallest to largest:

After we arrange, we get: \(\displaystyle 2,3,4,6,6,6,7,8,8,23,26,88,111\).

Step 2: To find the range, subtract the largest number from the smallest number.

\(\displaystyle Range=111-2=109\)

The range of the data set is \(\displaystyle 109\).

Example Question #2 : Range & Iqr

What is the range of the numbers: \(\displaystyle 2,3,7,9,14,11,100,99,62\)

Possible Answers:

\(\displaystyle 98\)

\(\displaystyle 100\)

\(\displaystyle 97\)

\(\displaystyle 96\)

Correct answer:

\(\displaystyle 98\)

Explanation:

Step 1: Re-write all numbers in order from smallest to largest

\(\displaystyle 2,3,7,9,11,14,62,99,100\).

Step 2: Subtract the largest number and smallest number

\(\displaystyle 100-2=98\)

The range is \(\displaystyle 98\).

Example Question #31 : Statistics

What is the range of the set: {\(\displaystyle 2,4,6,5,7,9,11,31,13,-2\)}

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 33\)

\(\displaystyle 11\)

\(\displaystyle -2\)

Correct answer:

\(\displaystyle 33\)

Explanation:

Step 1: Arrange the numbers from smallest to largest:

We get: \(\displaystyle -2,2,4,5,6,7,9,11,13,31\)

Step 2: Find the range.. To find this, subtract the biggest number from the smallest number

\(\displaystyle Range=31-(-2)=31+2=33\)

The range is \(\displaystyle 33\)

Example Question #41 : Probability & Statistics

Find the range of the set of numbers: \(\displaystyle \{2,4,5,6,7,2,11,-3\}\)

Possible Answers:

\(\displaystyle 15\)

\(\displaystyle 9\)

\(\displaystyle 14\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 14\)

Explanation:

Step 1: Arrange the numbers from smallest to largest. If the numbers are already written that way, then skip this step..

The numbers need to be arranged.. We will get: \(\displaystyle \{-3,2,2,4,5,6,7,11\}\)

Step 2: To find the range, subtract the smallest number from the biggest number...

So, \(\displaystyle 11-(-3)\implies 11+3\implies 14\)

The range of this set of numbers is \(\displaystyle 14\)...

Example Question #1 : Range & Iqr

What is the range of the numbers: \(\displaystyle \{2,4,5,6,7,8,9\}\)

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 7\)

\(\displaystyle 6\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 7\)

Explanation:

Step 1: See if the numbers are in order..

The numbers are in order from smallest to largest..

Step 2: Subtract the largest number and the smaller number:

\(\displaystyle 9-2=7\)

\(\displaystyle 7\) is the range.

Example Question #5 : Range & Iqr

What is the range of: \(\displaystyle \{2,4,7,-1,11,-6\}\)

Possible Answers:

\(\displaystyle 17\)

\(\displaystyle 14\)

\(\displaystyle 18\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 17\)

Explanation:

Step 1: Rearrange the numbers from smallest to largest:

After rearranging, we have: \(\displaystyle \{-6,-1,2,4,7,11\}\)

Step 2: Find the smallest number:

The smallest number is \(\displaystyle -6\).

Step 3: Find the largest number:

The largest number is \(\displaystyle 11\).

Step 4: Subtract the smallest number from the smallest number:

\(\displaystyle 11-(-6)=11+6=17\)

The range is \(\displaystyle 17\).

Example Question #2 : Range & Iqr

Find the range of: \(\displaystyle \{2,3,4,5,5,6,7,8,9,11\}\)

Possible Answers:

\(\displaystyle 10\)

\(\displaystyle 9\)

\(\displaystyle 8\)

\(\displaystyle 7\)

Correct answer:

\(\displaystyle 9\)

Explanation:

Step 1: Locate the smallest and largest numbers in the set above...

Largest is \(\displaystyle 11\), smallest is \(\displaystyle 2\)

Step 2: To find the range, subtract smallest from largest...

Range=\(\displaystyle 11-2=9\)

Example Question #3 : Range & Iqr

What is the range of the set, \(\displaystyle \large \{\}\)?

Possible Answers:

\(\displaystyle \large 1\)

Does Not Exist

\(\displaystyle \large 2\)

\(\displaystyle \large 0\)

Correct answer:

Does Not Exist

Explanation:

Step 1: Define Range of a set..

You can calculate the range by subtracting the smallest number from the largest number in the set..

Step 2: There are no numbers in this set. This set is also known as the empty set..

The range of a set that has no elements does not exist.

Example Question #44 : Probability & Statistics

If \(\displaystyle \large Q_1=12.5, Q_3=16.5\), find the IQR (Inter-Quartile Range)

Possible Answers:

\(\displaystyle \large 16.5\)

\(\displaystyle \large 20.5\)

\(\displaystyle \large 4\)

\(\displaystyle \large 8.5\)

Correct answer:

\(\displaystyle \large 4\)

Explanation:

Step 1: To find the Inter-Quartile Range, we need \(\displaystyle \large Q_1\) and \(\displaystyle \large Q_3\).

The formula for the Inter-Quartile Range is: \(\displaystyle \large Q_3-Q_1\).

Step 2: Plug in the given values of \(\displaystyle \large Q_1, Q_3\) to the equation...

\(\displaystyle \large Q_3-Q_1=16.5-12.5=4\)

So, the IQR=\(\displaystyle \large 4\)

Example Question #10 : Range & Iqr

Find the range: 

\(\displaystyle \{2,2,4,4,6,7,9,1,8,3,11,-7,12\}\)

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 15\)

\(\displaystyle 13\)

\(\displaystyle 17\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 19\)

Explanation:

Rearrange the numbers in the set from smallest to largest:

\(\displaystyle \{-7,1,2,2,3,4,4,6,7,8,9,11,12\}\)

To find the range, subtract the smallest number from the bigger number:

\(\displaystyle 12-(-7)=12+7=19\)

The range is \(\displaystyle 19\).

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