Box And Whisker Plots

BY:Katie BensonStephanie Ko

Natalie Zglinicki

Definition

• A plot that represents a distribution by a box, the ends of which mark the maximum and minimum values, and in which the median and first and third quartiles are marked by lines parallel to the ends.

• A single set of data is required to make this graph.

Why Use a Box and Whisker Plot?

• They are very effective and easy to read. The graph summarizes data from multiple sources and displays the results in a single graph. It is easy to compare data from different categories.

Examples

How to Create the Graph

Part 1 (Setting up the data):

When constructing a box and whisker plot, you must first find the median, the upper quartile, and

the lower quartile. Median

First find the median. The median is the

value exactly in the middle of an ordered set of

numbers.

Upper QuartileWhen finding the Upper quartile,

only consider the numbers to the

right of the median. Find the median of this set

of numbers. That is your upper

quartile.

Lower QuartileWhen finding the

lower quartile, only consider the

numbers to the left of the median. Find the median of this set of numbers.

That is your lower quartile.

How to Create the GraphPart 2 (Constructing the graph)

1. Make a line graph with a scale that will suit your data well.

2. Draw a short vertical line above your median.

3. Draw a short vertical line above your upper and lower quartiles.

4. Connect the vertical lines with two horizontal lines (One on the top and one on the bottom).

5. Mark the highest and lowest number in the data on the line graph with a dot.

6. Connect these dots to the upper and lower quartile lines that you made in step 3.

7. Notice how the plot looks like a box with whiskers. That is why it is called a box and whisker plot.

8. Here is an example:

Advantages and Disadvantages

Advantages

Represents the median very well

A good visual representation of how the data is spread out and how much variation there is.

Disadvantages

Does not show exact values clearly

Only shows a simple summary of the results

Problem

• Find the interquartile range of the graph (Formula: Q3 – Q1

=Interquartile)

Number of Pets

. .

0 1 2 3 4 5 6 7 8 9 10

. .

0 1 2 3 4 5 6 7 8 9 10

Problem Answered

After finding the median, the lower quartile, and the upper quartile, put the

quartiles into the formula to find the interquartile.

Q3 – Q1 =Interquartile 2-1 = 1

One is the Interquartile.

Works Cited

• http://dictionary.reference.com/browse/box+plot

• http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/box-whisker-plot.html

• http://www.webquest.hawaii.edu/kahihi/mathdictionary/images/boxplot.png

• http://www.srh.noaa.gov/images/tae/Fig2.jpg

• http://sph.bu.edu/otlt/lamorte/EP713/Web_Pages/BS704_SummarizingData/BS704_SummarizingData7.html

•http://images.sodahead.com/polls/000543969/polls_cat_1341_811773_answer_6_xlarge.jpeg

•http://www.netanimations.net/cats.htm