Finding the Interquartile Range 1

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Question 1 of 6

1. Question
Find the interquartile range from the data set below.

$9$ $3$ $8$ $7$ $6$ $8$ $4$ $6$ $2$ $10$ $9$
- $\text(IQR )=$ (5)
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Interquartile Range

$\text(IQR )=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$2$ $3$ $4$ $6$ $6$ $7$ $8$ $8$ $9$ $9$ $10$

We can see that the value $7$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$2$ $3$ $4$ $6$ $6$ $=$ $\text(Lower Half)$

$8$ $8$ $9$ $9$ $10$ $=$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$2$ $3$ $4$ $6$ $6$

$8$ $8$ $9$ $9$ $10$

$\text(Lower Quartile)$ $=$ $4$

$\text(Upper Quartile)$ $=$ $9$

Finally, use the formula to get the interquartile range.

$\text(IQR)$ $=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$ Interquartile Range formula

$=$ $9$ $-$ $4$ Substitute values

$=$ $5$

$\text(IQR)=5$
Question 2 of 6

2. Question
Find the interquartile range from the data set below.

$4$ $4$ $4$ $5$ $6$ $6$ $6$ $7$ $7$ $7$ $7$
- $\text(IQR )=$ (3)
Correct

Keep Going!

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Interquartile Range

$\text(IQR )=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, identify the median of the data set.

$4$ $4$ $4$ $5$ $6$ $6$ $6$ $7$ $7$ $7$ $7$

We can see that the value $6$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$4$ $4$ $4$ $5$ $6$ $=$ $\text(Lower Half)$

$6$ $7$ $7$ $7$ $7$ $=$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$4$ $4$ $4$ $5$ $6$

$6$ $7$ $7$ $7$ $7$

$\text(Lower Quartile)$ $=$ $4$

$\text(Upper Quartile)$ $=$ $7$

Finally, use the formula to get the interquartile range.

$\text(IQR)$ $=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$ Interquartile Range formula

$=$ $7$ $-$ $4$ Substitute values

$=$ $3$

$\text(IQR)=3$

Question 3 of 6

Find the interquartile range from the data set below.

Animal	Years	Animal	Years
Average Lifespan
Golden Hamster	4	Hog	18
Tasmanian Tiger	7	Eclectus Parrot	20
Cottontail	10	Teal	20
Fox	14	Domestic Pigeon	26
Grey Cheeked Parrot	15	Deer	35
Squirrel	16

$\text(IQR )=$ (10)

Question 4 of 6

4. Question
Find the interquartile range of the dot plot.
- $\text(IQR )=$ (10.5)
Correct

Great Work!

Incorrect

Interquartile Range

$\text(IQR )=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, take note that there is a total of $17$ scores on the dot plot, which is an odd number.

Therefore, the median of the data set will be the score on the $9th$ position.

$\text(Median)$ $=$ $46$

The median divides the data set into two quartiles, each with $8$ values.

To find the lower and upper quartiles, find the median of both the lower and greater halves.

$\text(Lower Quartile)$ $=$ $(40+41)/2$

$=$ $40.5$

$\text(Upper Quartile)$ $=$ $(50+52)/2$

$=$ $51$

Finally, use the formula to get the interquartile range.

$\text(IQR)$ $=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$ Interquartile Range formula

$=$ $51$ $-$ $40.5$ Substitute values

$=$ $10.5$

$\text(IQR)=10.5$
Question 5 of 6

5. Question
Find the interquartile range from the data set below.

$6$ $8$ $3$ $2$ $6$ $7$ $12$ $4$ $6$ $7$
- $\text(IQR )=$ (3)
Correct

Correct!

Incorrect

Interquartile Range

$\text(IQR )=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$2$ $3$ $4$ $6$ $6$ $6$ $7$ $7$ $8$ $12$

We can see that the value $6$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$2$ $3$ $4$ $6$ $6$ $=$ $\text(Lower Half)$

$6$ $7$ $7$ $8$ $12$ $=$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$2$ $3$ $4$ $6$ $6$

$6$ $7$ $7$ $8$ $12$

$\text(Lower Quartile)$ $=$ $4$

$\text(Upper Quartile)$ $=$ $7$

Finally, use the formula to get the interquartile range.

$\text(IQR)$ $=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$ Interquartile Range formula

$=$ $7$ $-$ $4$ Substitute values

$=$ $3$

$\text(IQR)=3$
Question 6 of 6

6. Question
Find the interquartile range from the data set below.

$12$ $5$ $11$ $4$ $9$ $4$ $6$ $8$ $9$ $6$ $7$
- $\text(IQR )=$ (4)
Correct

Correct!

Incorrect

Interquartile Range

$\text(IQR )=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$4$ $4$ $5$ $6$ $6$ $7$ $8$ $9$ $9$ $11$ $12$

We can see that the value $7$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$4$ $4$ $5$ $6$ $6$ $=$ $\text(Lower Half)$

$8$ $9$ $9$ $11$ $12$ $=$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$4$ $4$ $5$ $6$ $6$

$8$ $9$ $9$ $11$ $12$

$\text(Lower Quartile)$ $=$ $5$

$\text(Upper Quartile)$ $=$ $9$

Finally, use the formula to get the interquartile range.

$\text(IQR)$ $=$ $\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$ Interquartile Range formula

$=$ $9$ $-$ $5$ Substitute values

$=$ $4$

$\text(IQR)=4$

$4$	$7$	$10$	$14$	$15$
$18$	$20$	$20$	$26$	$35$

Finding the Interquartile Range 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Interquartile Range

Remember

2. Question

Keep Going!

Interquartile Range

Remember

3. Question

Excellent!

Interquartile Range

Remember

4. Question

Great Work!

Interquartile Range

Remember

5. Question

Correct!

Interquartile Range

Remember

6. Question

Correct!

Interquartile Range

Remember

Quizzes

$2$	$3$	$4$	$6$	$6$	$=$	$\text(Lower Half)$
$8$	$8$	$9$	$9$	$10$	$=$	$\text(Greater Half)$

$\text(IQR)$	$=$	$\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$	Interquartile Range formula
	$=$	$9$ $-$ $4$	Substitute values
	$=$	$5$

$\text(Lower Quartile)$	$=$	$10$
$\text(Upper Quartile)$	$=$	$20$

$2$	$3$	$4$	$6$	$6$	$=$	$\text(Lower Half)$
$6$	$7$	$7$	$8$	$12$	$=$	$\text(Greater Half)$

$4$	$4$	$5$	$6$	$6$	$=$	$\text(Lower Half)$
$8$	$9$	$9$	$11$	$12$	$=$	$\text(Greater Half)$