GMAT Math : Calculating range

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Descriptive Statistics

Consider the following set of numbers:

85, 87, 87, 82, 89

What is the range?

Possible Answers:

\displaystyle 85

\displaystyle 87

\displaystyle 3

\displaystyle 7

Correct answer:

\displaystyle 7

Explanation:

The range is the difference between the maximum and minimum value.

\displaystyle Range=89-82=7

Example Question #1 : Range

What is the range for the following data set:

\displaystyle 1,2,8,9,7,4,1,1,3,2,3

Possible Answers:

\displaystyle 2

\displaystyle 8

\displaystyle 1

\displaystyle 4

Correct answer:

\displaystyle 8

Explanation:

The range is the highest value number minus the lowest value number in a sorted data set:

\displaystyle 1,2,8,9,7,4,1,1,3,2,3

We need to sort the data set:

\displaystyle 1,1,1,2,2,3,3,4,7,8,9

\displaystyle range=9-1=8

Example Question #1 : Calculating Range

What is the range for the following set:

\displaystyle {63,49,68,59,29,62,46,5}

Possible Answers:

\displaystyle -58

\displaystyle 58

\displaystyle 59

\displaystyle 63

Correct answer:

\displaystyle 63

Explanation:

The range is the difference between the highest and lowest number.

First sort the set:

\displaystyle {5,29,46,49,59,62,63,68}

\displaystyle 68-5=63

Example Question #1 : Descriptive Statistics

Below is the stem-and-leaf display of a set of test scores.

\displaystyle \left.\begin{matrix} 4\\ 5\\ 6\\ 7\\ 8 \end{matrix}\right|\begin{matrix} \textrm{2 5}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \;\\ \textrm{4 4 7 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \\ \textrm{0 1 2 2 4 5 8 8 9}\\ \textrm{3 5 5 8} \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{7 }\; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \end{matrix}

What is the range of this set of scores?

Possible Answers:

\displaystyle 50

\displaystyle 52

\displaystyle 40

\displaystyle 45

\displaystyle 42

Correct answer:

\displaystyle 45

Explanation:

The range of a data set is the difference of the highest and lowest scores,

The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. The highest and lowest scores represented are 87 and 42, so the range is their difference: \displaystyle 87 - 42 = 45.

Example Question #2 : Range

Below is the stem-and-leaf display of a set of test scores.

\displaystyle \left.\begin{matrix} 4\\ 5\\ 6\\ 7\\ 8 \end{matrix}\right|\begin{matrix} \textrm{2 5}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \;\\ \textrm{4 4 7 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \\ \textrm{0 1 2 2 4 5 8 8 9}\\ \textrm{3 5 5 8} \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{7 }\; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \end{matrix}

What is the interquartile range of these test scores?

Possible Answers:

\displaystyle 16

\displaystyle 14

\displaystyle 9

\displaystyle 19

\displaystyle 12

Correct answer:

\displaystyle 14

Explanation:

The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. This stem-and-leaf display represents twenty scores.

The interquartile range is the difference of the third and first quartiles.

The third quartile is the median of the upper half, or the upper ten scores. This is the arithmetic mean of the fifth- and sixth-highest scores. These scores are 73 and 69, so the mean is \displaystyle \left (73 +69 \right )\div 2 = 71

The first quartile is the median of the lower half, or the lower ten scores. This is the arithmetic mean of the fifth- and sixth-lowest scores. Both of these scores are the same, however - 57.

The interquartile range is therefore the difference of these numbers: \displaystyle 71-57 = 14

Example Question #1 : Calculating Range

Consider the data set \displaystyle \left \{ 1, -2, 3, -4, 5, -6, 7, -8, 9, -10 \right \}.

What is its midrange?

Possible Answers:

\displaystyle -4.5

\displaystyle 0

\displaystyle -1

\displaystyle -0.5

\displaystyle -5.5

Correct answer:

\displaystyle -0.5

Explanation:

The midrange of a data set is the arithmetic mean of its greatest element and least element. Here, those elements are \displaystyle 9 and \displaystyle -10, so we can find the midrange as follows:

\displaystyle \left [9 + (-10) \right ]\div 2 = -1\div 2 = -0.5

Example Question #3 : Descriptive Statistics

Set 1: 5, 13, -2, -1, 19, 27

Set 2: 6, -3, 23, 15, m, 1

What should the value of \displaystyle m be if we want the ranges of both sets of number to be equal?

Possible Answers:

\displaystyle -4

\displaystyle 25

\displaystyle -2

\displaystyle 30

\displaystyle -6

Correct answer:

\displaystyle -6

Explanation:

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

The range of set 1 is:

 \displaystyle 27-(-2)=29

The range of the second set, ignoring the value of m is: 

\displaystyle 23-(-3)=26

We need to either subtract 3 from the lowest number in set Set 2 or add 3 to the highest number in Set 2 to get the value of m such that the range of both sets are equal.

\displaystyle m=(-3)-3=-6 \rightarrow range =23-(-6)=29 

or

\displaystyle m=23+3=26 \rightarrow range = 26-(-3)=29 

Example Question #4 : Calculating Range

Calculate the range of the following set of data:

\displaystyle (12, 15, 22, 24, 17, 9, 27, 21, 16, 23, 14)

Possible Answers:

\displaystyle 16

\displaystyle 18

\displaystyle 22

\displaystyle 21

\displaystyle 17

Correct answer:

\displaystyle 18

Explanation:

The range of a set of data is the difference between its highest value and its lowest value, as this describes the range of values spanned by the set. A quick way to calculate the range is to locate the lowest value in the set and subtract it from the highest value, but let's arrange the set in increasing order to visualize the problem first:

\displaystyle (9, 12, 14, 15, 16, 17, 21, 22, 23, 24, 27)

Now we can see that the lowest value in the set is 9, and the highest value in the set is 27, so the range of the set is:

\displaystyle 27 - 9 = 18

Example Question #1 : Descriptive Statistics

Calculate the range of the following set of data:

\displaystyle \begin{Bmatrix} 41, 28, 37, 41, 29, 33, 31, 40, 53, 49, 38, 42 \end{Bmatrix}

Possible Answers:

\displaystyle 28

\displaystyle 53

\displaystyle 49

\displaystyle 42

\displaystyle 25

Correct answer:

\displaystyle 25

Explanation:

The range of a set of data is the difference between its smallest and greatest values. We can first look through the set for the greatest value, which we can see is 53. We then look through the set for the smallest value, which we can see is 28. The range of the set is then:

\displaystyle 53-28=25

Example Question #1 : Descriptive Statistics

Determine the mean for the following set of numbers.

\displaystyle {6,2,5,5,8,4}

Possible Answers:

\displaystyle 2

\displaystyle 5

\displaystyle 4

\displaystyle 8

\displaystyle 6

Correct answer:

\displaystyle 6

Explanation:

To find the range, simply subract the smallest number from the largest. Therefore:

\displaystyle 8-2=6

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