Box and Whisker Plots

Module I, Lesson 5Online AlgebraVHS@PWCS

Box and Whisker Plots

A Box and Whisker Plot is a diagram that divides a set of data into 4 parts using

the median and the quartiles.

MinimumMaximum

Upper QuartileLower Quartile

Median

Median ReviewRecall from lesson 1.3, that a median is the number in the middle of a set

of data, when it is put in order.

Find the median of the following data:24, 36, 21, 17, 18, 15, 29, 30, 15, 37

1. Put the numbers in order from least to greatest.

2. Find the number in the middle.

3. Since there is no number in the middle, we find the mean of the 2 middle numbers.

1. 15, 15, 17, 18, 21, 24, 29, 30, 36, 37

3. (21 + 24)/2

45/2

22.5, is the median!

Lower Quartile

Lower quartile – median of the lower half of the data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Here is the middle (median)17 is the median of the

bottom half of the data. Therefore it is the Lower

quartile

Upper Quartile

Upper quartile – median of the upper half of the data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Here is the middle (median)

30 is the median of the bottom half of the data. Therefore it is the Upper

Quartile

What do you need for a Box and Whisker Plot?

1. Number Line

2. Minimum : smallest number

3. Lower quartile (LQ)

4. Median

5. Upper quartile (UQ)

6. Maximum: largest number.

7. Interquartile Range: UQ-LQ

The box goes around these!

The whiskers go from the minimum to the lower quartile and the upper quartile to the maximum

Let’s make a Box and Whisker Plot.

Here is our data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Step 1 – a number line

Our data goes from 15 to 37, our number line can go from 14 to 38, with an interval of 2

14 18 22 26 30 34 38

Let’s make a Box and Whisker Plot. Here is our data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Step 2 – Find the Values neededFrom our earlier calculations:

• Minimum – 15

• Lower Quartile – 17

• Median – 22. 5

• Upper Quartile – 30

• Maximum -37

•Interquartile Range-13

Let’s make a Box and Whisker Plot.

Here is our data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Step 3 – Plot the points a little above our number line

14 18 22 26 30 34 38

• Minimum – 15

• Lower Quartile – 17

• Median – 22. 5

• Upper Quartile - 30

• Maximum - 37

Let’s make a Box and Whisker Plot.

Here is our data

15, 15, 17, 18, 21, 24, 29, 30, 36, 37

Step 4– Draw the box and whiskers

14 18 22 26 30 34 38

• Minimum – 15

• Lower Quartile – 17

• Median – 22. 5

• Upper Quartile - 30

• Maximum - 37

Try this:

Create a box-and-whisker plot of the following data (click for you answer when finished).

8, 15.5, 14, 14, 16, 18, 16.7, 15, 11.4, 16, 7

Is yours the same?

8, 15.5, 14, 14, 16, 18, 16.7, 15, 11.4, 16, 7

7, 8, 11.4, 14, 14, 15, 15.5, 16, 16, 16.7, 18

Lower Quartile Median Upper Quartile

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

Data and Box-and-Whisker Plots A box and whisker plot breaks the data into 4

equal parts. 25% of the data is on the whisker from the

minimum to the lower quartile 25% of the data is in the box from the lower

quartile to the median 25% of the data is in the box from the median to

the upper quartile 25% of the data is on the whisker from the

upper quartile to the maximum.

What do you know.

If 240 people at six flags were stopped and asked their age, how many people are older than 15? 15 is the median and half of the data is above that so 120

people are older than 15. Of those people how many were between 11 ½ and 15.

There are 60 people in that age range. (240/4)

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

What you don’t know.

If you are only given a box-and-whisker plot, you cannot see the following: Mean – you need the individual data points and also the total Mode – again you need the individual points

You can however find the range (maximum – minimum) Or in this case 18 – 7, or 11.

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

Box-and-Whisker Recap

A box-and-whisker plot divides data into 4 equal parts.

It will show the following: minimum, lower quartile, median, upper quartile, and maximum, You cannot find the mean or mode if you don’t have the individual data points

You can find the range by Maximum - minimum

You can find the interquartile range by Upper quartile – lower quartile