Create and Interpret Box & Whisker Plots 3

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Question 1 of 7

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

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

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

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

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

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

We can see that the values $color(crimson)(12)$ and $color(crimson)(13)$ are the middle values of the data set.

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

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

$=$ $12.5$

The median divides the data set into two quartiles, each with $4$ values.

$10$ $11$ $12$ $12$ $=$ $\text(Lower Half)$

$13$ $13$ $15$ $19$ $=$ $\text(Greater Half)$

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

$10$ $11$ $12$ $12$

$13$ $13$ $15$ $19$

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

$=$ $11.5$

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

$=$ $14$

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.

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

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

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

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

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

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

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

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

$=$ $42.5$

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

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

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

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

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

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

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.

$\text(Range )=$ (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.

$\text(IQR )=$ (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.

$\text(IQR )=$ (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.
- $\text(Median )=$ (6)
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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 $color(tomato)(6)$ on the number line.

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

$\text(Median)=6$
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.
- $\text(Median )=$ (57, 56)
Correct

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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 $color(tomato)(57)$ on the number line.

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

$\text(Median)=57$

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

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

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

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

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

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

	$=$	$11.5$

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

	$=$	$14$

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

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

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

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

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

	$=$	$12.5$

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

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

	$=$	$42.5$