A box plot is a graph that shows the frequency of numeric data values. It can be drawn either horizontally or vertically. It is referred to as a Box-and-Whisker Plot.

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Box Plot
The Role of Box Plots in Comparing Multiple Data Sets

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Definition
One of the best ways to analyze any process is to plot the data on a graph
or chart.
Box Plot 2
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X
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X
X
X
X
X
X
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Definition
A box plot is a graph that shows the frequency of numeric data values.
Box Plot 3
Also referred to as a Box-and-
Whisker Plot as it displays the
data in a box-and-whiskers
format.

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Applications
Mainly used to explore data as well as to present the data in an easy and
understandable manner.
Box Plot 4
Box plots are widely used in
statistics, process improvement,
scientific research, economics,
and in social and human sciences

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Vertical vs. Horizontal
Box plots can be drawn either vertically or horizontally.
Box Plot 5
The length of the box plot indicates the spread of the data.

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Characteristics
They provide a quick way for examining the central tendency and variation
present in the data.
Box Plot 6
* * Outliers are usually
plotted as asterisks
A wider range boxplot indicates more variability.

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Characteristics
Box plots are useful when comparing between several data sets.
Box Plot 7
A B C D
In terms of central tendency and variability.

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Characteristics
The same continuous data can be presented graphically using histograms
and box plots.
Box Plot 8
Mean
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Characteristics
Less detailed than histograms and take up less space which make them
more practical when comparing multiple data sets.
Box Plot 9

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Uses
Used to check if there is a significant difference in the process after
implementing process improvement.
Box Plot 10
BEFORE
AFTER
In terms of central tendency and variability.

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Structure
A box plot is made up of a box and two whiskers.
Box Plot 11
Box Whisker
Whisker
Interquartile Range
The maximum length of a whisker is limited to 1.5 times the interquartile range (IQR).

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Structure
Box plots summarize key statistics from the data.
Box Plot 12
Median Maximum value
Minimum value
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Lower quartile Upper quartile
The middle line is the median of the data points.

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Structure
The data is plotted such as . . .
The middle 50% of the data points
The top 25% of the data
points
The bottom 25% of the
data points
25% 25%
Quartile Group 4
Quartile Group 1
Interquartile Range
Note: When the median line is not present in the box plot, it suggests that it coincides
with one of the quartiles.
Box Plot 13

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Structure
Sometimes the mean is displayed with a special character.
Box Plot 14
Median
Mean
Other character can indicate the mean such as a diamond or a plus.

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Structure
Any data beyond the whiskers are considered outliers.
Box Plot 15
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Outlier values
If the values are real, you should
investigate what was going on in
the process at that time.
Outliers often reflect errors in data
recording or data entry

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Structure
Box Plot 16
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Outlier
Median
Mean
25% 25%
Quartile Group 4
Quartile Group 1
Interquartile Range
25%
25%
Maximum value
Minimum value Lower quartile Upper quartile
Box
Whisker
●

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Data Size
Like histograms, used for moderate to large amount of data.
Box Plot 17
N = 40 N = 14
The size of the box plot can vary significantly if the data size is too small.

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Individual Value Plots
Individual Value Plots are preferred over boxplots when representing small
amount of data.
Box Plot 18

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Symmetric Distribution
Can tell whether the distribution is symmetrical or skewed.
Box Plot 19
Symmetric
Non symmetric
Mean Median
In a symmetric distribution, the mean and median are nearly the same, and the two
whiskers has almost the same length.

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Example – Crop Yield
The following box plots display the yield of a crop resulting from the
application of two different fertilizers.
Box Plot 20
Fertilizer #2 appears to yield higher crop
yields than Fertilizer #1. What other
comments would you make about the
above box plots? Think about the
variation as well as the presence of any
unusual values or outliers.
Fertilizer 2
Fertilizer 1
55
50
45
40
35
Yield
Data source: Minitab
What other comments would you make
about the above boxplots?
Think about the variation as well as the
presence of any unusual values.

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Example – Diabetes Test
The below box plots illustrate an analysis that was conducted for diagnosing
the presence of diabetes at a workplace.
Box Plot 21
Female Male
500
400
300
200
100
0
Gender
Test
results
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It is evident that females have in general
higher glucose levels than males.
To confirm the statistical significance of
this difference, ANOVA can be applied to
compare the means between the two
groups.

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Further Information
There are many applications and online services that allow the creation of
box plots quickly and easily (such as Minitab, JMP, and SPSS).
Box Plot 22

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