Create and Interpret Box & Whisker Plots

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Question 1 of 10

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

$6$ $5$ $7$ $3$ $3$ $2$ $2$ $5$ $4$ $3$ $4$ $7$
- 1.
- 2.
- 3.
- 4.
Hint

Help Video

Correct

Excellent!

Incorrect

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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.

$\text(Highest Score)$ $=$ $7$

$\text(Lowest Score)$ $=$ $2$

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

$2$ $2$ $3$ $3$ $3$ $4$ $4$ $5$ $5$ $6$ $7$ $7$

We can see that the values $4$ and $4$ are the middle values of the data set.

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

$\text(Median)$ $=$ $(4+4)/2$

$=$ $4$

The median divides the data set into two quartiles, each with $6$ values.

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

$4$ $5$ $5$ $6$ $7$ $7$ $=$ $\text(Greater Half)$

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

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

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

$\text(Lower Quartile)$ $=$ $(3+3)/2$

$=$ $3$

$\text(Upper Quartile)$ $=$ $(5+6)/2$

$=$ $5.5$

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 10

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

$5$ $6$ $7$ $4$ $9$ $12$ $6$ $2$ $11$
- 1.
- 2.
- 3.
- 4.
Hint

Help Video

Correct

Nice Job!

Incorrect

Help Video

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.

$\text(Highest Score)$ $=$ $12$

$\text(Lowest Score)$ $=$ $2$

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

$2$ $4$ $5$ $6$ $6$ $7$ $9$ $11$ $12$

We can see that the values $6$ is the middle values of the data set.

Therefore, the median of the data set is $6$

$\text(Median)$ $=$ $6$

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

$2$ $4$ $5$ $6$ $=$ $\text(Lower Half)$

$7$ $9$ $11$ $12$ $=$ $\text(Greater Half)$

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

$2$ $4$ $5$ $6$

$7$ $9$ $11$ $12$

$\text(Lower Quartile)$ $=$ $(4+5)/2$

$=$ $4.5$

$\text(Upper Quartile)$ $=$ $(9+11)/2$

$=$ $10$

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 10

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

$6$ $10$ $4$ $5$ $7$ $11$ $13$ $7$
- 1.
- 2.
- 3.
- 4.
Hint

Help Video

Correct

Well Done!

Incorrect

Help Video

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.

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

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

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

$4$ $5$ $6$ $7$ $7$ $10$ $11$ $13$

We can see that the values $7$ and $7$ are the middle values of the data set.

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

$\text(Median)$ $=$ $(7+7)/2$

$=$ $7$

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

$4$ $5$ $6$ $7$ $=$ $\text(Lower Half)$

$7$ $10$ $11$ $13$ $=$ $\text(Greater Half)$

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

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

$7$ $10$ $11$ $13$

$\text(Lower Quartile)$ $=$ $(5+6)/2$

$=$ $5.5$

$\text(Upper Quartile)$ $=$ $(10+11)/2$

$=$ $10.5$

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 4 of 10

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

$31$ $36$ $47$ $47$ $48$ $52$ $52$ $54$ $54$
- 1.
- 2.
- 3.
- 4.
Correct

Great Work!

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.

$\text(Highest Score)$ $=$ $54$

$\text(Lowest Score)$ $=$ $31$

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

Next, identify the median of the data set.

$31$ $36$ $47$ $47$ $48$ $52$ $52$ $54$ $54$

We can see that the values $48$ is the middle values of the data set.

Therefore, the median of the data set is $48$

$\text(Median)$ $=$ $48$

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

$31$ $36$ $47$ $47$ $=$ $\text(Lower Half)$

$52$ $52$ $54$ $54$ $=$ $\text(Greater Half)$

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

$31$ $36$ $47$ $47$

$52$ $52$ $54$ $54$

$\text(Lower Quartile)$ $=$ $(36+47)/2$

$=$ $41.5$

$\text(Upper Quartile)$ $=$ $(52+54)/2$

$=$ $53$

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 5 of 10

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

$16$ $18$ $16$ $21$ $19$ $11$ $17$ $14$

$15$ $16$ $22$ $17$ $15$ $16$ $22$ $12$
- 1.
- 2.
- 3.
- 4.
Correct

Correct!

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.

$\text(Highest Score)$ $=$ $22$

$\text(Lowest Score)$ $=$ $11$

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

$11$ $12$ $14$ $15$ $15$ $16$ $16$ $16$

$16$ $17$ $17$ $18$ $19$ $21$ $22$ $22$

We can see that the values $16$ and $16$ are the middle values of the data set.

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

$\text(Median)$ $=$ $(16+16)/2$

$=$ $16$

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

$11$ $12$ $14$ $15$ $15$ $16$ $16$ $16$ $=$ $\text(Lower Half)$

$16$ $17$ $17$ $18$ $19$ $21$ $22$ $22$ $=$ $\text(Greater Half)$

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

$11$ $12$ $14$ $15$ $15$ $16$ $16$ $16$

$16$ $17$ $17$ $18$ $19$ $21$ $22$ $22$

$\text(Lower Quartile)$ $=$ $(15+15)/2$

$=$ $15$

$\text(Upper Quartile)$ $=$ $(18+19)/2$

$=$ $18.5$

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 6 of 10

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

Life Expectancy

Country Years Country Years

Somalia 50 Indonesia 72

Lesotho 51 Montenegro 74.5

Chad 51 Croatia 77.5

Guinea 55 Israel 82.1

Cameroon 61.5 Iceland 83.3

Bangladesh 70
- 1.
- 2.
- 3.
- 4.
Correct

Keep Going!

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.

$\text(Highest Score)$ $=$ $50$

$\text(Lowest Score)$ $=$ $83.3$

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

Next, identify the median of the data set.

$50$ $51$ $51$ $55$ $61.5$ $70$ $72$ $74.5$ $77.5$ $82.1$ $83.3$

We can see that the values $70$ is the middle values of the data set.

Therefore, the median of the data set is $70$

$\text(Median)$ $=$ $70$

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

$50$ $51$ $51$ $55$ $61.5$ $=$ $\text(Lower Half)$

$72$ $74.5$ $77.5$ $82.1$ $83.3$ $=$ $\text(Greater Half)$

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

$50$ $51$ $51$ $55$ $61.5$

$72$ $74.5$ $77.5$ $82.1$ $83.3$

$\text(Lower Quartile)$ $=$ $51$

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

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.

Life Expectancy
Country	Years	Country	Years
Somalia	50	Indonesia	72
Lesotho	51	Montenegro	74.5
Chad	51	Croatia	77.5
Guinea	55	Israel	82.1
Cameroon	61.5	Iceland	83.3
Bangladesh	70

Question 7 of 10

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

Name	Age	Country	Years
Nobel Laureates
Mikhail Sergeyevich Gorbachev	59	Robert Alexander Mundell	67
Thomas Crombie Schelling	84	Robert Floyd Curl Jr.	63
Rigoberta Menchú Tum	33	Richard Axel	58
Mairéad Corrigan-Maguire	32	Koichi Tanaka	43
Hans Georg Dehmelt	67	George Elwood Smith	79
Doris May Lessing	88	Vernon Lomax Smith	75
Werner Arber	49	Leo Esaki	48
Russell Alan Hulse	61.5	Hamilton Othanel SMith	47

Question 8 of 10

8. Question
The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the range.
- $\text(Range )=$ (9)
Hint

Help Video

Correct

Excellent!

Incorrect

Help Video

Range Formula

$\text(Highest Score)$ $-$ $\text(Lowest Score)$

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

$\text(Highest Score)$ $=$ $16$

$\text(Lowest Score)$ $=$ $7$

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

$\text(Range)$ $=$ $\text(Highest Score)$ $-$ $\text(Lowest Score)$ Finding the range

$=$ $16$ $-$ $7$ Substitute values

$=$ $9$ Evaluate

$\text(Range)=9$
Question 9 of 10

9. Question
The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the interquartile range.
- $\text(IQR )=$ (4.5)
Hint

Help Video

Correct

Well Done!

Incorrect

Help Video

Interquartile Range

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

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

$\text(Upper Quartile)$ $=$ $14.5$

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

Use the formula to get the interquartile range.

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

$=$ $14.5$ $-$ $10$ Substitute values

$=$ $4.5$ Evaluate

$\text(IQR)=4.5$
Question 10 of 10

10. Question
The box and whisker plot below represents the number of goals scored per month by a soccer team. Find the median.
- $\text(Median )=$ (12)
Hint

Help Video

Correct

Great Work!

Incorrect

Help Video

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 $12$ on the number line.

Therefore, the median of the box and whisker plot is $12$ .

$\text(Median)=12$

$32$	$33$	$43$	$43$	$47$	$48$	$49$	$58$	$=$	$\text(Lower Half)$
$59$	$63$	$67$	$67$	$75$	$79$	$84$	$88$	$=$	$\text(Greater Half)$

$32$	$33$	$43$	$43$	$47$	$48$	$49$	$58$
$59$	$63$	$67$	$67$	$75$	$79$	$84$	$88$

Create and Interpret Box & Whisker Plots

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Quiz summary

Information

1. Question

Hint

Excellent!

2. Question

Hint

Nice Job!

3. Question

Hint

Well Done!

4. Question

Great Work!

5. Question

Correct!

6. Question

Keep Going!

7. Question

Fantastic!

8. Question

Hint

Excellent!

Range Formula

Remember

9. Question

Hint

Well Done!

Interquartile Range

Remember

10. Question

Hint

Great Work!

Quizzes

$\text(Lower Quartile)$	$=$	$(3+3)/2$

	$=$	$3$

$\text(Upper Quartile)$	$=$	$(5+6)/2$

	$=$	$5.5$

$2$	$4$	$5$	$6$	$=$	$\text(Lower Half)$
$7$	$9$	$11$	$12$	$=$	$\text(Greater Half)$

$\text(Lower Quartile)$	$=$	$(4+5)/2$

	$=$	$4.5$

$\text(Upper Quartile)$	$=$	$(9+11)/2$

	$=$	$10$

$31$	$36$	$47$	$47$	$=$	$\text(Lower Half)$
$52$	$52$	$54$	$54$	$=$	$\text(Greater Half)$

$\text(Lower Quartile)$	$=$	$(36+47)/2$

	$=$	$41.5$

$\text(Upper Quartile)$	$=$	$(52+54)/2$

	$=$	$53$

$16$	$18$	$16$	$21$	$19$	$11$	$17$	$14$
$15$	$16$	$22$	$17$	$15$	$16$	$22$	$12$

$\text(Lower Quartile)$	$=$	$(15+15)/2$

	$=$	$15$

$\text(Upper Quartile)$	$=$	$(18+19)/2$

	$=$	$18.5$

$50$	$51$	$51$	$55$	$61.5$	$=$	$\text(Lower Half)$
$72$	$74.5$	$77.5$	$82.1$	$83.3$	$=$	$\text(Greater Half)$

$\text(Lower Quartile)$	$=$	$(43+47)/2$

	$=$	$45$

$\text(Upper Quartile)$	$=$	$(67+75)/2$

	$=$	$71$

$\text(Range)$	$=$	$\text(Highest Score)$ $-$ $\text(Lowest Score)$	Finding the range
	$=$	$16$ $-$ $7$	Substitute values
	$=$	$9$	Evaluate

$\text(Highest Score)$	$=$	$7$
$\text(Lowest Score)$	$=$	$2$

$\text(Highest Score)$	$=$	$12$
$\text(Lowest Score)$	$=$	$2$

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

$\text(Highest Score)$	$=$	$54$
$\text(Lowest Score)$	$=$	$31$

$\text(Upper Quartile)$	$=$	$14.5$
$\text(Lower Quartile)$	$=$	$10$

$\text(IQR)$	$=$	$\text(Q)_\text(Upper)$ $-$ $\text(Q)_\text(Lower)$	Interquartile Range formula
	$=$	$14.5$ $-$ $10$	Substitute values
	$=$	$4.5$	Evaluate