The document explains histograms as graphical representations that summarize the distribution of continuous data, highlighting their use in various fields such as statistics and scientific research. It details how to construct a histogram, its applications in identifying data characteristics like central tendency and outliers, and its limitations with small data sizes. Additionally, it provides examples of histograms used for analyzing cable diameters and diagnosing diabetes.

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Histogram
The Role of Histograms in Exploring Data Insights

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Introduction
One of the best ways to analyze any process is to plot the data on a graph
or chart.
Histogram 2
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X
X
X
X
X
X
X
X
X
X
X

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Definition
A histogram is a graphical way that summarizes the important aspects of
the distribution of continuous data.
Histogram 3
A type of
bar chart

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Definition
Histograms are sometimes called Frequency Plots as they show the
frequency of continuous data values on a graph.
Histogram 4
Number
of
occurrence
(frequency)
|––––––––– Value bins –––––––––|
While Pareto charts plot the frequency of count data!

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Vertical vs. Horizontal
Can be drawn either vertically or horizontally.
Histogram 5
|–––––– FREQUENCY ––––––|
|–––––
FREQUENCY
–––––|
The height of the column indicates how often that data value occurred.

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Applications
Histograms are widely used in statistics, scientific research, higher
education, process improvement, and in social and human sciences.
Histogram 6
Mainly used to explore data as well
as to present the data in an easy
and understandable manner

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Characteristics
Plotting the data using a histogram allows to explore many characteristics
of the data . . .
Histogram 7
Central tendency
and the amount of
spread
Minimum and
maximum values
The shape of data
(symmetric or
skewed)
Whether it’s
unimodal, bimodal
or multimodal

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Characteristics
It allows to visually and quickly assess . . .
Histogram 8
Spread Outliers
Gap
Center
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The central tendency and
the amount of spread in the
data
The shape of the
distribution
The presence of gaps,
outliers or unusual data
points

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Characteristics
It allows to visually and quickly assess . . .
Histogram 9
Spread Outliers
Gap
Center
*
Shows where most of
the data exists

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Spread Outliers
Gap
Center
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Characteristics
It allows to visually and quickly assess . . .
Creates a picture of the
variation in a process.
Histogram 10
Enables to quickly identify the
spread of the data

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Characteristics
It allows to visually and quickly assess . . .
Histogram 11
Spread Outliers
Gap
Center
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Overall shape shows
how the data is
distributed

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Characteristics
It allows to visually and quickly assess . . .
Histogram 12
Spread Outliers
Gap
Center
*
Helps to find unusual
data points and
outliers that may need
further investigation

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Characteristics
It allows to visually and quickly assess . . .
Histogram 13
Spread Outliers
Gap
Center
*
Helps to find unusual
data points and
outliers that may need
further investigation
Overall shape shows
how the data is
distributed
Enables to quickly identify the
spread of the data
Shows where most of
the data exists

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Uses
Used as the first step to determine the underlying probability distribution
of a data set.
Histogram 14
Allows to shape the sample data to make predictions and draw conclusions about
an entire population.

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Uses
Histograms are used to identify . . .
Histogram 15
Whether the process is capable or not
Whether variability is within specification limits
Whether there is a shift in the process
Whether you can apply certain statistical tests
Patterns that provide clues to certain types of problems

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Uses
Used to verify that the changes made were a real improvement.
Histogram 16
Before
LSL USL
After
LSL USL

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Data Size
Ideal to represent moderate to large amount of data.
Histogram 17
N = 40 N = 14
In practice, a sample size of at least 30 data values would be sufficient.

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Data Size
It may not accurately display the distribution shape if the data size is too
small.
Histogram 18
Dot plots are preferred over histograms when representing small amount of data.

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Steps for Manually Constructing a Histogram
Histogram 19
Collect the data set and prepare it for the analysis
• Create a summary table of the data.
Data

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Steps for Manually Constructing a Histogram
Histogram 20
Draw a horizontal line and divide it into equal intervals or bins (12 intervals for example)
• The total width should be equal to the range of the data.

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Steps for Manually Constructing a Histogram
Histogram 21
Draw bars above each bin to represent the frequency of the data values within each interval
• The bars should be adjacent with no gaps between them (to indicate the
continuity of the data).

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Steps for Manually Constructing a Histogram
Histogram 22
Calculate the mean of the data
• Indicate the standard deviation and the specification limits.
Mean
LSL

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Example – Cable Diameters
The following is a histogram that represents the distribution of cable
diameters for a manufacturing process.
Histogram 23
0.60
0.58
0.56
0.54
0.52
0.50
20
1 5
1 0
5
0
Mean 0.5465
StDev 0.01934
N 100
Diameter of cable
Frequency
Data source: Minitab

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Example – Cable Diameters
The result can be summarized using day to day language such as:
Histogram 24
0.60
0.58
0.56
0.54
0.52
0.50
20
1 5
1 0
5
0
Mean 0.5465
StDev 0.01934
N 100
Diameter of cable
Frequency
Data source: Minitab
“The distribution looks
symmetric around the
cable diameter mean
(0.546 cm) and appears
to fit the Normal
Distribution”

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Example – Presence of Diabetes
This histogram illustrates an analysis
that was conducted for diagnosing
the presence of diabetes at a
workplace.
Histogram 25
0 100 200 300 400 500
120
100
80
60
40
20
Mean 99.65
StDev 36.58
N 310
Test results
Frequency
Note that the data distribution
exhibits a right-skewed pattern. It
looks more like an exponential
distribution which is normal for this
type of data.

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Further Information
Histogram 26
Histograms, however, can’t see changes and trends
over time
Histograms like control charts can be used to assess improvement
overtime

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Further Information
You can illustrate a stratification factor in histograms.
Histogram 27
MORNING SHIFT EVENING SHIFT NIGHT SHIFT

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Further Information
There are many applications and online services that allow the creation of
histograms quickly and automatically (such as Minitab, JMP, and SPSS).
Histogram 28

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