Create and Interpret Box & Whisker Plots 3

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Question 1 of 7

Create a box and whisker plot using the data set below.

11

$11$

12

$12$

19

$19$

10

$10$

13

$13$

15

$15$

12

$12$

13

$13$

Incorrect

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

First, find the highest and the lowest score.

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$19$ $19$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$10$ $10$

Create a number line with with ascending values from the lowest to highest scores

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

10

$10$

11

$11$

12

$12$

12

$12$

13

$13$

13

$13$

15

$15$

19

$19$

We can see that the values

12

$color(crimson)(12)$ and

13

$color(crimson)(13)$ are the middle values of the data set.

To find the median, we add the two middle values and divide it by

2

$2$

$Median$ $\text(Median)$	$=$ $=$	$\frac{12 + 13}{2}$ $(12+13)/2$

	$=$ $=$	$12.5$ $12.5$

The median divides the data set into two quartiles, each with

4

$4$ values.

$10$ $10$	$11$ $11$	$12$ $12$	$12$ $12$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$13$ $13$	$13$ $13$	$15$ $15$	$19$ $19$	$=$ $=$	$Greater Half$ $\text(Greater Half)$

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

$10$ $10$	$11$ $11$	$12$ $12$	$12$ $12$
$13$ $13$	$13$ $13$	$15$ $15$	$19$ $19$

$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$\frac{11 + 12}{2}$ $(11+12)/2$

	$=$ $=$	$11.5$ $11.5$

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$\frac{13 + 15}{2}$ $(13+15)/2$

	$=$ $=$	$14$ $14$

Now, mark the number line with dots for the lowest and highest scores of the data set.

Next, mark the lower and upper quartile with a line, and connect them to form a box.

Finally, mark the median with a line inside the box.

Also connect the dots to the box to make the whiskers.

Question 2 of 7

2. Question
Create a box and whisker plot using the data set below.

$41$ $41$ $43$ $43$ $41$ $41$ $48$ $48$ $37$ $37$ $49$ $49$ $48$ $48$ $42$ $42$ $47$ $47$ $42$ $42$
- 1.
- 2.
- 3.
- 4.
Correct

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Incorrect

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

First, find the highest and the lowest score.

$Highest Score$ $\text(Highest Score)$ $=$ $=$ $49$ $49$

$Lowest Score$ $\text(Lowest Score)$ $=$ $=$ $37$ $37$

Create a number line with with ascending values from the lowest to highest scores

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

$37$ $37$ $41$ $41$ $41$ $41$ $42$ $42$ $42$ $42$ $43$ $43$ $47$ $47$ $48$ $48$ $48$ $48$ $49$ $49$

We can see that the values $42$ $color(crimson)(42)$ and $43$ $color(crimson)(43)$ are the middle values of the data set.

To find the median, we add the two middle values and divide it by $2$ $2$

$Median$ $\text(Median)$ $=$ $=$ $\frac{42 + 43}{2}$ $(42+43)/2$

$=$ $=$ $42.5$ $42.5$

The median divides the data set into two quartiles, each with $5$ $5$ values.

$37$ $37$ $41$ $41$ $41$ $41$ $42$ $42$ $42$ $42$ $=$ $=$ $Lower Half$ $\text(Lower Half)$

$43$ $43$ $47$ $47$ $48$ $48$ $48$ $48$ $49$ $49$ $=$ $=$ $Greater Half$ $\text(Greater Half)$

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

$37$ $37$ $41$ $41$ $41$ $41$ $42$ $42$ $42$ $42$

$43$ $43$ $47$ $47$ $48$ $48$ $48$ $48$ $49$ $49$

Now, mark the number line with dots for the lowest and highest scores of the data set.

Next, mark the lower and upper quartile with a line, and connect them to form a box.

Finally, mark the median with a line inside the box.

Also connect the dots to the box to make the whiskers.

Question 3 of 7

The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the range.

$Range =$ $\text(Range )=$ (9)

Incorrect

Range Formula

Highest Score - Lowest Score

$color(deeppink)(\text(Highest Score)) – color(darkviolet)(\text(Lowest Score))$

Remember

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

The lowest and highest scores are indicated by the whiskers of the box and whisker plot

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$13$ $13$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$4$ $4$

Subtract the lowest score from the highest score to get the range

$Range$ $\text(Range)$	$=$ $=$	$Highest Score - Lowest Score$ $color(deeppink)(\text(Highest Score)) – color(darkviolet)(\text(Lowest Score))$	Finding the range
	$=$ $=$	$13 - 4$ $color(deeppink)(13)-color(darkviolet)(4)$	Substitute values
	$=$ $=$	$9$ $9$

Range = 9

$\text(Range)=9$

Question 4 of 7

The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the interquartile range.

$IQR =$ $\text(IQR )=$ (11)

Incorrect

Interquartile Range

IQR = Q_{Upper} - Q_{Lower}

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

Remember

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

The lower and upper quartiles are indicated by the outer lines of the box and whisker plot

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$53$ $53$
$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$42$ $42$

Use the formula to get the interquartile range.

$IQR$ $\text(IQR)$	$=$ $=$	$Q_{Upper} - Q_{Lower}$ $color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))$	Interquartile Range formula
	$=$ $=$	$53 - 42$ $color(deeppink)(53)-color(darkviolet)(42)$	Substitute values
	$=$ $=$	$11$ $11$

IQR = 11

$\text(IQR)=11$

Question 5 of 7

The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the interquartile range.

$IQR =$ $\text(IQR )=$ (23.5)

Incorrect

Interquartile Range

IQR = Q_{Upper} - Q_{Lower}

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

Remember

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

The lower and upper quartiles are indicated by the outer lines of the box and whisker plot

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$77.5$ $77.5$
$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$54$ $54$

Use the formula to get the interquartile range.

$IQR$ $\text(IQR)$	$=$ $=$	$Q_{Upper} - Q_{Lower}$ $color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))$	Interquartile Range formula
	$=$ $=$	$77.5 - 54$ $color(deeppink)(77.5)-color(darkviolet)(54)$	Substitute values
	$=$ $=$	$23.5$ $23.5$

IQR = 23.5

$\text(IQR)=23.5$

Question 6 of 7

6. Question
The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the median.
- $Median =$ $\text(Median )=$ (6)
Correct

Keep Going!

Incorrect

The median is the middle score in a data set.

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

The median is indicated by the line inside the box and whisker plot

The line inside the box points to the score $6$ $color(tomato)(6)$ on the number line.

Therefore, the median of the box and whisker plot is $6$ $6$ .

$Median = 6$ $\text(Median)=6$
Question 7 of 7

7. Question
The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the median.
- $Median =$ $\text(Median )=$ (57, 56)
Correct

Keep Going!

Incorrect

The median is the middle score in a data set.

A box-and-whisker plot shows a five-point summary of the lowest score, lower quartile, median, upper quartile and highest score.

The median is indicated by the line inside the box and whisker plot

The line inside the box points to the score $57$ $color(tomato)(57)$ on the number line.

Therefore, the median of the box and whisker plot is $57$ $57$ .

$Median = 57$ $\text(Median)=57$

Create and Interpret Box & Whisker Plots 3

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Quiz summary

Information

1. Question

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2. Question

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3. Question

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Range Formula

Remember

4. Question

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Interquartile Range

Remember

5. Question

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Interquartile Range

Remember

6. Question

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7. Question

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Quizzes

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$49$ $49$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$37$ $37$

$Median$ $\text(Median)$	$=$ $=$	$\frac{42 + 43}{2}$ $(42+43)/2$

	$=$ $=$	$42.5$ $42.5$

$37$ $37$	$41$ $41$	$41$ $41$	$42$ $42$	$42$ $42$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$43$ $43$	$47$ $47$	$48$ $48$	$48$ $48$	$49$ $49$	$=$ $=$	$Greater Half$ $\text(Greater Half)$