How To Draw The Box Plot Corresponding To The Given Five-number Summary

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Section iii.five: The Five-Number Summary and Boxplots

Objectives

By the cease of this lesson, you will be able to...

compute the 5-number summary
draw and translate boxplots

For a quick overview of this department, watch this short video summary:

The Five-Number Summary

The five-number summary of a set of data consists of the smallest data value, Q_ane, the median, Q₃, and the largest value of the data.

Example 1

To illustrate, let's again look at those examination scores from Example 4 in Department iii.4.

48	57	58	65	68	69	71	73	73
74	75	77	78	78	78	79	80	85
87	88	89	89	89	95	96	97	99

Find the five-number summary.

[ reveal answer ]

From Case 4 in Section 3.4, we already know that Q₁ = 71, median 78, and Q₃ = 89. We only need the maximum and minimum, so the five-number summary is:

minimum = 48
Q₁ = 71
median 78
Q₃ = 89
maximum = 99

Boxplots

Using the five-number summary and the fences, nosotros can create a new graph called a boxplot.

Drawing a Boxplot

Step 1: Determine the 5-number summary and the lower and upper fences.
Step 2: Draw a horizontal line and label it with an appropriate scale.
Pace 3: Draw vertical lines at Q₁ , Chiliad, and Q₃. Enclose these vertical lines in a box.
Step four: Depict a line from Q1 to the smallest data value that is within the lower fence. Similarly, depict a line from Q3 to the largest value that is within the upper argue.
Step v: Any values exterior the fences are outliers and are marked with an asterisk (*).

A typical boxplot volition wait something like this:

boxplot

Case 2

To illustrate, let'south again expect at those exam scores from Example 4 in Section 3.4.

48	57	58	65	68	69	71	73	73
74	75	77	78	78	78	79	eighty	85
87	88	89	89	89	95	96	97	99

Take a moment and try to sketch a boxplot of this data prepare, following the description above.

[ reveal answer ]

Using the 5-number summary from Example 1 above and the outlier calculation from Instance v in Section iii.4, we have the following information:

minimum = 48
Q_one = 71
median 78
Q₃ = 89
maximum = 99
Lower fence = 44
Upper contend = 116

A boxplot would so look something like this:

example boxplot

Engineering

Here's a quick overview of how to create box plots in StatCrunch.

Enter or import the data.
Select Graphics > Box Plot.
Select the column(south) you want to create a box plot for.
Click Next.
Check "Use fences to place outliers" and click Adjacent.
Enter any modifications and click Next.
Choose a color scheme, if you lot wish, and click Create Graph!
You can then choose Options > Copy to copy the box plot for apply elsewhere.

You tin can likewise visit the video page for links to come across videos in either Quicktime or iPod format.

Boxplots and Distribution Shape

The last affair nosotros want to talk about in Chapter iii is the human relationship between the shape of a boxplot and the shape of the distribution.

In Section two.2, nosotros talked about distribution shape, showing the following four standards:

Let's now see how these are related to boxplots. Here's some data from your text:

Symmetric distributions

Distribution	Boxplot
Q_one is equally far from the median every bit Q₃ is	The median line is in the center of the box
The minimum is every bit far from the median as the maximum is	The left whisker is equal in length to the correct whisker

symmetric

Skewed left distributions

Distribution	Boxplot
Q₁ is farther from the median every bit Q₃ is	The median line is to the correct of heart in the box
The minimum is further from the median every bit the maximum is	The left whisker is longer than the right whisker

left-skewed

Skewed right distributions

Distribution	Boxplot
Q₁ is closer to the median than Q₃ is	The median line is to the left of center in the box
The minimum is closer to the median as the maximum is	The left whisker is shorter than the correct whisker