Basic Arithmetic : Range

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #341 : Basic Arithmetic

John is \(\displaystyle 12\) years old. He has a younger sister who is \(\displaystyle 4\), a younger brother who is \(\displaystyle 7\), and an older sister who is \(\displaystyle 14\). What is the range of John and his siblings' ages?

Possible Answers:

\(\displaystyle 2\) years

\(\displaystyle 8\) years

\(\displaystyle 10\) years

\(\displaystyle 14\) years

\(\displaystyle 7\) years

Correct answer:

\(\displaystyle 10\) years

Explanation:

The youngest of John and his siblings is his younger sister, who is \(\displaystyle 4\). The oldest of John and his siblings is his older sister, who is \(\displaystyle 14\). To find the range we need to subtract the lowest value from the highest value.

This gives us a range of,

 \(\displaystyle 14-4=10\) years.

Example Question #342 : Basic Arithmetic

Robert has a data set consisting of the following numbers: 

\(\displaystyle 29, 45, 566, 28, 35, 222, 45, 56, 753, 567, 32, 567, 223, 93\)

What is the range of the data set?

Possible Answers:

\(\displaystyle 725\)

\(\displaystyle 531\)

\(\displaystyle 721\)

\(\displaystyle 673\)

\(\displaystyle 753\)

Correct answer:

\(\displaystyle 725\)

Explanation:

The correct answer is 725. The range of any data set can be obtained by subtracting the smallest number from the largest number.

In this case, the smallest number is 28 and the largest number is 753.

The following subtraction problem gives us the answer:

\(\displaystyle 753-28 = 725\).

Example Question #343 : Basic Arithmetic

Karen plays on her school's basketball team. She keeps track of the number of points she scores in each game. For the past 6 games, she scored 23 points, 10 points, 34 points, 9 points, 12 points, and 11 points. What is the range for the number of points she scored over the past 6 games?

Possible Answers:

\(\displaystyle 34\)

\(\displaystyle 23\)

\(\displaystyle 24\)

\(\displaystyle 25\)

Correct answer:

\(\displaystyle 25\)

Explanation:

To find the range, place the numbers in numerical order:

\(\displaystyle 9,10,11,12,23,34\)

Then, subtract the smallest value from the largest value.

\(\displaystyle 34-9=25\)

Example Question #1 : Range

Jessica wanted to keep track of how well she was doing in her basketball games, so she started recording the number of points she scored each game. In her past six games, she scored \(\displaystyle 12\) points, \(\displaystyle 5\) points, \(\displaystyle 19\) points, \(\displaystyle 31\) points, \(\displaystyle 18\) points, and \(\displaystyle 17\) points. What is the range of the number of points Jessica has scored in the past six games?

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 26\)

\(\displaystyle 31\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 26\)

Explanation:

To find the range of a set of numbers, you need to first find the smallest and the largest numbers.

In Jessica's case, our smallest data point is 5 and the largest is 31.

Then, to find the range, subtract these two numbers.

\(\displaystyle 31-5=26\)

Example Question #344 : Basic Arithmetic

Loretta tracks how much money her ice cream shop makes in a week. On Monday, she made \(\displaystyle \$1700\). On Tuesday, she made \(\displaystyle \$1627\). On Wednesday, she made \(\displaystyle \$918\). On Thursday, she made \(\displaystyle \$1001\). On Friday, she made \(\displaystyle \$2102\). On Saturday, she made \(\displaystyle \$3019\). On Sunday, she made \(\displaystyle \$1291\). What is the range of the money she made in this given week?

Possible Answers:

\(\displaystyle \$3019\)

\(\displaystyle \$1728\)

\(\displaystyle \$2101\)

\(\displaystyle \$2018\)

Correct answer:

\(\displaystyle \$2101\)

Explanation:

To find the range, you need to first find the largest and the smallest number in the data set.

In this case, the largest number is 3019 and the smallest number is 918.

To find the range, subtract the smallest number from the largest.

\(\displaystyle 3019-918=2101\)

Example Question #344 : Basic Arithmetic

In a calculus class with \(\displaystyle 18\) students, the highest score on the most recent test was a \(\displaystyle 99\) while the lowest score on the most recent test was a \(\displaystyle 53\). What is the range on the most recent test?

Possible Answers:

\(\displaystyle 53\)

\(\displaystyle 18\)

\(\displaystyle 46\)

\(\displaystyle 99\)

Correct answer:

\(\displaystyle 46\)

Explanation:

To find the range of a set of numbers, subtract the smallest number from the largest number.

\(\displaystyle 99-53=46\)

Example Question #2 : Range

Observe the following table:

Client          Age
Marsha 14
Tom 13
Alice 65
Brandy 34
Candy 23
James 43
Brady 19

Find the range for the ages of the clients in the table?

Possible Answers:

\(\displaystyle 62\)

\(\displaystyle 52\)

\(\displaystyle 13\)

\(\displaystyle 50\)

\(\displaystyle 47\)

Correct answer:

\(\displaystyle 52\)

Explanation:

Let us start by identifying the maximum and minimum values of the list of values.

The maximum is 65 and the minimum is 13.

The range is computed by substracting the minimum from the maximum, which gives us:

\(\displaystyle R= \text{Max}-\text{Min}\)

\(\displaystyle =65-13\)

\(\displaystyle =52\)

Example Question #5 : Data Properties

Find the range of the set:

\(\displaystyle 4, 5, 6, 12, 15, 18, 19, 23, 26, 27, 31, 39, 41\)

Possible Answers:

\(\displaystyle 37\)

\(\displaystyle 38\)

\(\displaystyle 36\)

\(\displaystyle 34\)

Correct answer:

\(\displaystyle 37\)

Explanation:

To find the range of a set subtract the smallest number in the set from the largest number in the set:

\(\displaystyle {\color{Blue} 4}, 5, 6, 12, 15, 18, 19, 23, 26, 27, 31, 39, {\color{Green} 41}\)

The largest number is in green: \(\displaystyle 41\) 

The smallest number is in blue: \(\displaystyle 4\)

Therefore the range is as follows.

\(\displaystyle 41-4=37\)

Example Question #6 : Data Properties

Find the range of the set:

\(\displaystyle 12, 15, 16, 24, 25, 31, 36\)

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 23\)

\(\displaystyle 26\)

\(\displaystyle 25\)

Correct answer:

\(\displaystyle 24\)

Explanation:

To find the range of a set subtract the smallest number in the set from the largest number in the set:

\(\displaystyle {\color{Blue} 12}, 15, 16, 24, 25, 31, {\color{Green} 36}\)

The largest number is in green: \(\displaystyle 36\)

The smallest number is in blue: \(\displaystyle 12\)

Therefore the range is,

\(\displaystyle 36-12=24\).

Example Question #1 : Range

Find the range of the set:

\(\displaystyle 15, 24, 27, 28, 28, 39, 44, 47, 61, 77, 88\)

Possible Answers:

\(\displaystyle 77\)

\(\displaystyle 74\)

\(\displaystyle 69\)

\(\displaystyle 73\)

Correct answer:

\(\displaystyle 73\)

Explanation:

To find the range of a set subtract the smallest number in the set from the largest number in the set:

\(\displaystyle {\color{Blue} 15}, 24, 27, 28, 28, 39, 44, 47, 61, 77, {\color{Green} 88}\)

The largest number is in green: \(\displaystyle 88\)

The smallest number is in blue: \(\displaystyle 15\)

Therefore the range is,

\(\displaystyle 88-15=73\).

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