Box and Whisker Box and Whisker PlotsPlots

Box and Whisker PlotBox and Whisker Plot

A box and whisker plot is a diagram or A box and whisker plot is a diagram or graph that shows quartiles and graph that shows quartiles and extreme values of a set of data.extreme values of a set of data.

Five Number SummaryFive Number Summary

1. Median

2. LQ (Lower Quartile)

3. UQ (Upper Quartile)

4. Minimum (Lower Extreme)

5. Maximum (Upper Extreme)

LetLet’’s review how to s review how to find the Five find the Five Number Summary…Number Summary…

Here are the Here are the number of gold number of gold medals won by the medals won by the top 16 countries in top 16 countries in the 1992 summer the 1992 summer Olympics.Olympics.

Country# of Gold Medals

Unified Team 45

USA 37

Germany 33

China 16

Cuba 14

Hungary 11

S. Korea 12

France 8

Australia 7

Spain 13

Japan 3

Britain 6

Italy 6

Poland 3

Canada 6

Romania 4

First, put the numbers in order from least First, put the numbers in order from least to greatest.to greatest.

Second, find the median, lower quartile Second, find the median, lower quartile (LQ), and upper quartile (UQ).(LQ), and upper quartile (UQ).

9.5 9.5 MeMedd

5.5 5.5 LQLQ

15 15 UQUQ

Third, find the minimum & maximum.Third, find the minimum & maximum.

MinMin MaMaxx

This is called a “five number summary.”

Min = 3

LQ = 5.5

Med = 9.5

UQ = 15

Max = 45

3, 3, 4, 5, 4537,33,16,14,6, 6, 7, 8, 11,12, 13,

Before we can make the box plot, we Before we can make the box plot, we need to check for need to check for outliersoutliers..

An An outlieroutlier is a number that is 1.5 is a number that is 1.5 Interquartile Ranges (IQR) above the Interquartile Ranges (IQR) above the UQ and below the LQ.UQ and below the LQ.

Okay, now I am

lost!! IQR = UQ - LQIQR = UQ - LQ

Steps to Finding Steps to Finding OutliersOutliers

1. IQR = UQ - LQ1. IQR = UQ - LQ

2. IQR · 1.5 2. IQR · 1.5

3. Add answer from #2 to UQ.3. Add answer from #2 to UQ.

4. Subtract answer from #2 from LQ.4. Subtract answer from #2 from LQ.

Anything greater than your answer to Anything greater than your answer to #3 is an outlier.#3 is an outlier.

Anything less than your answer to #4 Anything less than your answer to #4 is also an outlier.is also an outlier.

Before we can draw the box and Before we can draw the box and whisker plot, we also need to find whisker plot, we also need to find outliersoutliers..

Min = 3

LQ = 5.5

Med = 9.5

UQ = 15

Max = 45

Outliers are numbers Outliers are numbers

that are 1.5 IQRthat are 1.5 IQR’’s above s above

or below LQ & UQ.or below LQ & UQ.

IQR = UQ - LQIQR = UQ - LQ15 - 5.5 = 9.515 - 5.5 = 9.59.5 ·1.5 = 9.5 ·1.5 = 14.2514.25

14.25 + 15 = 29.25

5.5 - 14.25 = -8.75

So… the outliers are…

x > 29.25 OR x < -8.75

3, 3, 4, 5, 6, 6, 7, 8, 11, 12, 13, 14, 16, 33, 37, 45

9.5 Med

5.5 LQ

15 UQ

Min Max

33, 37, and 45 are outliers for this data.33, 37, and 45 are outliers for this data.

Now we have all the information we Now we have all the information we need to draw the box and whisker need to draw the box and whisker

plot.plot.

To draw the box and whisker plot, you To draw the box and whisker plot, you need the five number summary and the need the five number summary and the outliers.outliers.

Min = 3

LQ = 5.5

Med = 9.5

UQ = 15

Max = 45

Outliers:

33, 37, 45

First, draw a number line that will First, draw a number line that will accommodate the data range.accommodate the data range.

0 5 10 15 20 25 30 35 40 45 50

LQ, Med, and UQ form the box.LQ, Med, and UQ form the box.

The outliers are marked with asterisks.The outliers are marked with asterisks.

** *

The The ““whiskerswhiskers”” connect the box with the connect the box with the last numbers that are not outliers.last numbers that are not outliers.

You have just drawn a box and whisker You have just drawn a box and whisker plot!plot!

0 5 10 15 20 25 30 35 40 45 50

** *

Box and whisker plots are divided into quartiles. Box and whisker plots are divided into quartiles. Each quartile contains 1/4 or 25% of the data.Each quartile contains 1/4 or 25% of the data.

Even though the quartiles do not appear to be Even though the quartiles do not appear to be equal, they all contain an equal amount of data.equal, they all contain an equal amount of data.

For this box and whisker plot...1st fourth of data:1st fourth of data: x < 5.5 x < 5.5

2nd fourth of data: 2nd fourth of data: 5.5 < x < 9.55.5 < x < 9.53rd fourth of data: 3rd fourth of data: 9.5 < x < 159.5 < x < 15

4th fourth of data:4th fourth of data: x > 15 x > 15

0 5 10 15 20 25 30 35 40 45 50

** *

Using the box and whisker plot:Using the box and whisker plot:

What percent of the teams won 6 and 15 gold medals?About 50%About 50%

What does the plot tell us about the upper half of the data compared to the lower half?The upper half is more spread out while The upper half is more spread out while the lower half is closely clustered the lower half is closely clustered together.together.

Here is the time in which 10 students ran a Here is the time in which 10 students ran a mile:mile:

Find the Find the ““five number five number summarysummary””, the outliers, , the outliers,

and draw a box and and draw a box and whisker plot of the data.whisker plot of the data.

Click when you are ready for the Click when you are ready for the answer.answer.

10, 12, 8, 10, 9, 10, 9, 11, 10, 18

10, 12,8, 10,9, 10,9, 11,10, 18

10 Med

LQ UQMin Max

Five Number Summary:

Min = 8

LQ = 9

Med = 10

UQ = 11

Max = 18

Outliers:

x < 6

x > 14

So… 18 is an outlier.

7 8 9 10 11 12 13 14 15 16 17 18 19

*

There are more examples of box There are more examples of box and whisker plots in your book.and whisker plots in your book.

Happy graphing!Happy graphing!