Box & Whisker PlotsSDAP 1.3 (Understand the meaning of, and be able to

compute the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set).

Heat vs. Lakers 3/4/12

T. Murphy0 points

S. Blake3 points

A. Goudelock7 points

A. Bynum16 points

K. Bryant33 points

Heat vs. Lakers 3/4/12

MinimumValue0

First Quartile3

Median7

ThirdQuartile

16

Maximum Value

33

What is a box & whisker plot?

A box-and-whisker plot ◦can be useful for handling many data values◦allow people to explore data and to draw

informal conclusions when two or more variables are present

◦show only certain statistics rather than all the data Think back on the Lakers… did the box-and-

whisker plot show rebounds? Fouls? Free throws?

Step One: Find the Median (middle)

The following numbers are the amount of marbles different boys own.68 34 54 82 18 93 87 78 61 85 100 27 52 59 91-------------------------------------------------------

To find the median, put the numbers in order & find the one in the exact middle18 27 34 52 54 59 61 68 78 82 85 87 91 93 100

Step Two: The Lower Quartile

Focus only on the values to the left of the median: 18 27 34 52 54 59 61

Now we need to find the median of these numbers◦Since they’re already in order it’s easy to see

the median of the values less than the median is 52

This value is called the “Lower Quartile”◦Think ahead: Using your knowledge of prefixes

and suffixes, what does ‘quartile’ mean and how will knowing this help us design our box-and-whisker plot?

Step Three: The Lower Quartile

Now consider only the values to the right of the median: 78 82 85 87 91 93 100

You should have noticed the median of this set of numbers is 87

This value is called the “Upper Quartile”

Wait a minute… Too easy right?

What happens if you’re finding the median in an ordered set with an even number of values?◦You must first take the average of the two

middle numbers. For example: 3, 5, 7, and 10.

Add the two middle numbers 5 + 7 = 12Divide your answer by the number of values added 12 / 2 = 66 is the average and yourmedian for this set.

Step Four: The Interquartile Range

You’re now ready to find the Interquartile Range (IQR).

The IQR is the difference between the upper quartile and the lower quartile.

In our case the IQR = 87 – 52 IQR = 35

The IQR is a very useful measurement because it is less influenced by extreme values, it limits the range to the middle 50% of the values.

Step Five: Draw Your Graph

X

Now you try!

#1

What is the median of the set of data below?

34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12

34

#2

What is the upper quartile of the set of data below?

34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12

41

#3

What is the maximum value (upper extreme) of the set of data below?

34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12

56

DROPS ON A PENNY! partner activity

You will need:◦Cup of water◦Penny◦Paper towel◦Eye dropper◦4 sticky notes◦Pencil

Directions

Working with a partner, take turns dropping one drop of water at a time on the penny.

Both partners count the drops as you go to assure for an accurate count.

When the water finally spills over the edge of the penny record on your sticky note how many drops you had before the water spilled

Each partner will take 2 turnsBe sure to dry the penny between turnsWhen your team is done, clean up and construct

a box-and-whisker plot for your information.◦When everyone is finished we will make one for the

class’ results!