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Algebra II : Range

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Example Questions

Example Question #1 : Data Properties

Suppose the ages of a college chemistry class were recorded and the ages reported were as follows: $\displaystyle 35, 60, 18, 19, 18, 24, 31, 44, 20, 18, 23, 32, 21.$

What is the range of this data?

Possible Answers:

$\displaystyle 42$

$\displaystyle 60$

$\displaystyle 18$

27.9 $\displaystyle 27.9$

$\displaystyle 23$

Correct answer:

$\displaystyle 42$

Explanation:

The range is calculated by subtracting the smallest value from the largest value: $\displaystyle 60-18=42$ .

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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:

$\displaystyle 47$

$\displaystyle 13$

$\displaystyle 50$

$\displaystyle 62$

$\displaystyle 52$

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:

$R= \text{Max}-\text{Min}$ $\displaystyle R= \text{Max}-\text{Min}$

=65-13 $\displaystyle =65-13$

=52 $\displaystyle =52$

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Example Question #1 : Data Properties

Observe the following list of terms:

$\displaystyle 10 ; 20 ; 13 ; 12 ; 14 ; x ; 19$

The range of this list of numbers is $\displaystyle 10$ . Which value can $\displaystyle x$ take?

Possible Answers:

$\displaystyle 8$

$\displaystyle 9$

$\displaystyle 21$

$\displaystyle 0$

$\displaystyle 17$

Correct answer:

$\displaystyle 17$

Explanation:

The range of this list of numbers is 10 which is obtained by doing 20-10.

This means that 20 and 10 are respectively the maximum and minimum values of the list of numbers.

Therefore x has to be a value between 10 and 20.

17 being the only value within this range it is therefore the right answer.

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Example Question #3 : Range

For a set of numbers $\left\{ a,a,a,b,b,b,b,c,c \right \}$ $\displaystyle \left\{ a,a,a,b,b,b,b,c,c \right \}$ where a<b<c $\displaystyle a< b< c$

and the set has the following values:

$\textup{median}=7$ $\displaystyle \textup{median}=7$

$\textup{mean}=8$ $\displaystyle \textup{mean}=8$

$\textup{range}=7$ $\displaystyle \textup{range}=7$

Determine the value of $\displaystyle c$ .

Possible Answers:

$\displaystyle 11$

$\displaystyle 7$

$\displaystyle 8$

$\displaystyle 13$

$\displaystyle 6$

Correct answer:

$\displaystyle 13$

Explanation:

{6,6,6,7,7,7,7,13,13}

median=7 so b=7

mean=8 so the sum of the set is 72.

72-4(7)=44

44=3a+2c

Range=7 so c-a=7

44=3a+2(a+7)

a=6 and c=13.

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Example Question #2 : Data Properties

$\left \{ 89, 98, 77, 92, 93 \right \}$ $\displaystyle \left \{ 89, 98, 77, 92, 93 \right \}$

Given the set of test scores, what is the range?

Possible Answers:

$\displaystyle 12$

$\displaystyle 1$

$\displaystyle 9$

$\displaystyle 16$

$\displaystyle 21$

Correct answer:

$\displaystyle 21$

Explanation:

The range is the difference between the smallest number and the largest number. The smallest value is 77, and the largest is 98.

98 – 77 = 21

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Example Question #1 : Range

The range of the following data set is 18. What is a possible value for $\displaystyle x$ ?

$\left \{ 3, -5, 7, 7, 5, 10, x, 1, -2 \right \}$ $\displaystyle \left \{ 3, -5, 7, 7, 5, 10, x, 1, -2 \right \}$

Possible Answers:

x=10 $\displaystyle x=10$

x=0 $\displaystyle x=0$

Cannot be determined

x=-8 $\displaystyle x=-8$

x = -13 $\displaystyle x = -13$

Correct answer:

x=-8 $\displaystyle x=-8$

Explanation:

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

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Example Question #3 : Data Properties

Hours_chart

The above chart shows a specific week of work at an advertising firm. What is the range of the hourly rates of the workers?

Possible Answers:

$\$20$ $\displaystyle \$20$

$\$25$ $\displaystyle \$25$

$\$40$ $\displaystyle \$40$

$\$35$ $\displaystyle \$35$

$\$30$ $\displaystyle \$30$

Correct answer:

$\$25$ $\displaystyle \$25$

Explanation:

The range is difference between the largest value and the smallest value.

$Largest=\$40$ $\displaystyle Largest=\$40$

$Smallest=\$15$ $\displaystyle Smallest=\$15$

$Range=Largest-Smallest=\$40-\$15=\$25$ $\displaystyle Range=Largest-Smallest=\$40-\$15=\$25$

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Example Question #4 : Data Properties

What is the range of the set $\left \{ -2,6,13,25,-2,4,11\right \}$ $\displaystyle \left \{ -2,6,13,25,-2,4,11\right \}$ ?

Possible Answers:

$\displaystyle 6$

$\displaystyle -2$

$\displaystyle 27$

7.9 $\displaystyle 7.9$

Correct answer:

$\displaystyle 27$

Explanation:

The range is defined as the difference between the highest and lowest numbers in a set. Here, the highest number is $\displaystyle 25$ and the lowest is $\displaystyle -2$ .

Therefore, the range is

$\displaystyle 25 - (-2)=27$

$\displaystyle -2$ is the mode, 7.9 $\displaystyle 7.9$ is the mean, and 6 is the median.

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Example Question #2 : Range

Find the range of the set:

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

Possible Answers:

$\displaystyle 36$

$\displaystyle 38$

$\displaystyle 34$

$\displaystyle 37$

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:

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

The largest number is in green: $\displaystyle 41$

The smallest number is in blue: $\displaystyle 4$

Therefore the range is as follows.

41-4=37 $\displaystyle 41-4=37$

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Example Question #3 : Range

Find the range of the set:

$\displaystyle 12, 15, 16, 24, 25, 31, 36$

Possible Answers:

$\displaystyle 26$

$\displaystyle 25$

$\displaystyle 23$

$\displaystyle 24$

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:

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

The largest number is in green: $\displaystyle 36$

The smallest number is in blue: $\displaystyle 12$

Therefore the range is,

$\displaystyle 36-12=24$ .

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Algebra II : Range

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Data Properties

Example Question #2 : Range

Example Question #1 : Data Properties

Example Question #3 : Range

Example Question #2 : Data Properties

Example Question #1 : Range

Example Question #3 : Data Properties

Example Question #4 : Data Properties

Example Question #2 : Range

Example Question #3 : Range

All Algebra II Resources

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