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

5. Maximum

Let’s review how to Let’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,

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

Min = 3

LQ = 5.5

Med = 9.5

UQ = 15

Max = 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 “whiskers” connect the box with the The “whiskers” connect the box with the minimum and maximum.minimum and maximum.

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 “five number Find the “five number summary” and draw a summary” and draw a

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

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!