histograms[1]

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Histograms: A Histograms: A Valuable Tool for Valuable Tool for Quality EvaluationQuality Evaluation

By Perry KatzBy Perry Katz

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OverviewOverview

1)1) What is a Histogram?What is a Histogram?2)2) What are some possible uses for a What are some possible uses for a

Histogram?Histogram?3)3) Where did the Histogram come Where did the Histogram come

from?from?4)4) How do Histograms work?How do Histograms work?5)5) A real world example.A real world example.6)6) An exercise.An exercise.

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What is a Histogram?What is a Histogram?

• A Histogram is a variation of a bar A Histogram is a variation of a bar chart in which data values are chart in which data values are grouped together and put into grouped together and put into different classes. different classes.

• This grouping allows you see how This grouping allows you see how frequently data in each class occur frequently data in each class occur in the data set.in the data set.

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What is a Histogram What is a Histogram (cont.)(cont.)

• Higher barsHigher bars represent represent more datamore data valuesvalues in a class. in a class.

• Lower barsLower bars represent represent fewer datafewer data valuesvalues in a class. in a class.

• On the next slide is an example of On the next slide is an example of what a Histogram looks like. what a Histogram looks like.

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Example of a HistogramExample of a Histogram

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Uses for a Histogram Uses for a Histogram

A Histogram can be used:A Histogram can be used:• to display large amounts of data values to display large amounts of data values

in a relatively simple chart form.in a relatively simple chart form.• to tell relative frequency of occurrence.to tell relative frequency of occurrence.• to easily see the distribution of the data.to easily see the distribution of the data.• to see if there is variation in the data.to see if there is variation in the data.• to make future predictions based on the to make future predictions based on the

data. data.

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Where did the Histogram Where did the Histogram Come From?Come From?

• The Histogram was first The Histogram was first implemented by Kaoru Isikawa, one implemented by Kaoru Isikawa, one of Japans’ most renowned experts of Japans’ most renowned experts on quality improvement.on quality improvement.

• Isikawa spent his life trying to Isikawa spent his life trying to improve quality in Japan. improve quality in Japan.

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Where did the Histogram Where did the Histogram Come From? (cont.)Come From? (cont.)

• His major contributions to quality His major contributions to quality improvement are known as the improvement are known as the basic seven tools of quality.basic seven tools of quality.

• Included in his basic seven tools of Included in his basic seven tools of quality is the Histogram.quality is the Histogram.

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How do Histograms Work?How do Histograms Work?

• First, you need need to pick a process to First, you need need to pick a process to analyze.analyze.

• Next, you need a large amount of data, Next, you need a large amount of data, at least 100 data values so that patterns at least 100 data values so that patterns can become visible.can become visible.

• Then, you need to assemble a table of Then, you need to assemble a table of the data values that you collected with the data values that you collected with regards to frequency of data values.regards to frequency of data values.

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How do Histograms Work? How do Histograms Work? (cont)(cont)

• Next, you need to calculate some Next, you need to calculate some statistics for the Histogram, including: statistics for the Histogram, including: mean, minimum, maximum, standard mean, minimum, maximum, standard deviation, class width, number of deviation, class width, number of classes, skewness, and kurtosis.classes, skewness, and kurtosis.

• Then, you actually create the Histogram Then, you actually create the Histogram using these statistics. using these statistics.

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• After you have created a After you have created a Histogram, it will take one of five Histogram, it will take one of five shapes:shapes:

• Normal DistributionNormal Distribution::

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• Positively SkewedPositively Skewed::

• Negatively SkewedNegatively Skewed::

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• Bi-Modal DistributionBi-Modal Distribution::

• Multi-Modal DistributionMulti-Modal Distribution::

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• Once your Histogram is complete, Once your Histogram is complete, you can analyze its shape, as well you can analyze its shape, as well as the statistics that you came up as the statistics that you came up with. with.

• This analysis will help you to make This analysis will help you to make better decisions toward quality better decisions toward quality improvements.improvements.

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Real World ExampleReal World Example• The next slide contains a real world The next slide contains a real world

example of a histogram. It plots the example of a histogram. It plots the relative frequency of the heights of relative frequency of the heights of some students based on the data below. some students based on the data below. Frequency:Height (feet): (Number of pupils) Relative frequency:0-2 0 02-4 1 14-5 4 85-6 8 166-8 2 2

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Real World ExampleReal World Example

• This Histogram is courtesy of http://www.gcsemaths.fsnet.co.uk/page5.htmlThis Histogram is courtesy of http://www.gcsemaths.fsnet.co.uk/page5.html

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ExerciseExercise

• A great exercise which would help you A great exercise which would help you better understand what a histogram is better understand what a histogram is all about can be found at :all about can be found at :

http://www.usfca.edu/histogram_explorer/he.htmlhttp://www.usfca.edu/histogram_explorer/he.html

Here you are walked through the making Here you are walked through the making of a histogram. You see all of the of a histogram. You see all of the aspects that I have discussed in this aspects that I have discussed in this tutorial.tutorial.

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SummarySummary

• After going through this tutorial After going through this tutorial you should have a better idea of:you should have a better idea of:

1)1) What a Histogram is.What a Histogram is.2)2) What a Histogram is used for.What a Histogram is used for.3)3) Where the Histogram came from.Where the Histogram came from.4)4) How Histograms work.How Histograms work.

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Histograms: A Histograms: A Valuable Tool for Valuable Tool for Quality EvaluationQuality Evaluation

By Perry KatzBy Perry Katz

histograms[1]

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