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LESSON: Box and Whisker Plots

Box and Whisker Plots

Site: Mountain Heights Academy OpenCourseWare
Course: Mathematics Essentials Q3 v2013
Book: LESSON: Box and Whisker Plots
Printed by: Guest user
Date: Sunday, 25 February 2018, 4:33 PM

Vocab/Objectives

  • Order a set of data to find the median, quartiles and extremes.
  • Draw a box-and-whisker plot to represent given data.
  • Identify the median, quartiles, and extremes given a box-and-whisker plot.
  • Compare and Interpret double box-and-whisker plots of real-world data.

Median
the middle score of a set of data.
Quartile
dividing a data into four sections.
Upper Quartile
the median of a quartile on the higher end of the range.
Lower quartile
the median of a quartile on the lower range
Extremes
the highest and lowest scores possible in a range of data.

WATCH: Construct a Box and Whisker Plot

READ: Order a Set of Data to Find the Median, Quartiles and Extremes

Order a Set of Data to Find the Median, Quartiles and Extremes

Today’s lesson focuses on data once again. This time, we will be building box-and-whisker plots. To understand a box-and-whisker plot there is some vocabulary to learn first. Our first key word when working with box-and-whisker plots is median.

When working with data, we often have series of numbers that tell us important information. Here is data set showing the number of hours that the average teenager works in a part time job.

16, 10, 8, 8, 11, 11, 12, 15, 10, 20, 6, 16, 8


To work with this set of data, the first thing that we need to do is to order the data. To order means that we write the data in order from least to greatest including any repeated numbers.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20


Next, we find the median. Remember that the median is the middle number in a set of data. Here there are 13 values. The median is 11.

The median is 11.


The next key term that we need to understand is a quartile. A quartile divides the data set into four parts. With the median, our data set is divided into two parts. The first part is the first half up to 10 and the second half starts at 11 and goes to 20. The median is in purple.

Take a look.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20


To use quartiles, we need to divide this data set into four sections not two. To do this, we find the median of the first half of the data and the median of the second half of the data. The median of the first half of the data is called the lower quartile. The median of the second half of the data is called the upper quartile.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20

Here the median is in red.

The lower quartile is the average between 8 and 8. The lower quartile is 8.

The upper quartile is the average between 15 and 16. The lower quartile is 15.5.


The next term that we need to know is the extremes. The term extreme refers to the lowest value in a data set, the lower extreme and the highest value in a data set the upper extreme.

In the set we just looked at, 6 is the lower extreme and 20 is the upper extreme.

READ: Draw a Box-and-Whisker Plot to Represent Given Data

Draw a Box-and-Whisker Plot to Represent Given Data

Now that we have identified all of the key parts of a box-and-whisker plot we can move on to drawing one. Here are the key things that we need to do BEFORE drawing a box-and-whisker plot.

We have this information for the data set that we looked at in the last section. Here is the data set again.

6, 8, 8, 8, 10, 10, 11, 11, 12, 15, 16, 16, 20


Here are the steps to drawing a box-and-whisker plot.

  1. Draw a number line labeled to show the range of data from least to greatest.
  2. Mark the median, the upper quartile, the lower quartile, the lower extreme and the upper extreme on the number line.
  3. Draw in a box around the quartiles. The median is the middle line of the two boxes.
  4. Then draw in the whiskers. These are lines that extend from each quartile to the upper and lower extremes.

Here is a picture of a number line with a completed box-and-whisker plot on it.

Now let’s examine this plot. The first box goes from the lower quartile 8 to the median 11. The second box goes from the median 11 to the upper quartile 15.5. The whiskers extend out from the lower quartile to the lower extreme of 6, and from the upper quartile to the upper extreme of 20.


READ: Identify the Median, Quartiles, and Extremes Given a Box-and-Whisker Plot

Identify the Median, Quartiles, and Extremes Given a Box-and-Whisker Plot

Now that you know how to draw a box-and-whisker plot and find the median, quartiles and extremes of a set of data, we can work the other way around too. We can look at a box-and-whisker plot to identify the median, quartiles and extremes.


We can use this chart to examine the data. The median divides the two boxes. The median here is 200. The lower quartile is 100 and the upper quartile is 300. The lower extreme is 50 and the upper extreme is 400.

We can use a box-and-whisker plot to analyze data, to show data in a visual way and to compare two sets of data.

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

CHECK Yourself! Box and Whisker Plots