Transcript Chapter 19

Data Analysis and Data
Chapter 19
Achieving Quality Through Continual
Claude W. Burrill / Johannes Ledolter
Published by John Wiley & Sons, Inc., 1999
Prepared by Dr. Tomi Wahlström,
University of Southern Colorado
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• Data need to be summarized and displayed
so that its meaning can be shared with all
parties involved
• 80-20 rule: 80% of what you are interested
in is concentrated in 20% of the
• Basic statistical principles must be
understood by everyone in the organization
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Organizing Data-The Pareto
• The relative frequencies are displayed in the
form of a bar chart, with the heights of the bars
representing the frequencies of the various
• It is easy to organize data by the type of defect:
• Collect data for the problem
• Classify the data into about a half-dozen categories, one
of which might be “other”
• List each class and the number of its members in order
starting with the most frequent class
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Data Presentation
• Since many people don’t feel comfortable
with numbers, graphical tools must be
employed to communicate data
• Due to desktop computers, drawing graphs
has become effective and efficient
improving the way data is presented
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Graphical Displays of a Data Set
• Time-sequence display
– Measurements plotted against time
• Dot diagram
– Each measurement is represented on a
horizontal line by a dot that indicates is
• Histogram
– Range of observations divided into nonoverlapping intervals
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Summary Statistics of a Data Set:
Descriptive Statistics
• Measures of central tendency
– Mean: sum of the data elements divided by the
number of data elements
– Median: middle-most data element after the
data have been arranged according to size
– Mode: data element appearing with the highest
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Descriptive Statistics
• Measures of Variability
– Variance: based on the squared differences
between the data elements and the average
– Standard deviation: square root of the variance
– Range: the difference between the largest and
the smallest data element
• Descriptive statistics help us track
performance over time
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Scatter Diagrams and Correlation
• Scatter diagrams help us in a graphical form
to see how two or more variables are
• Correlation coefficient is a numerical value
to represent this correlation
– It measures linear association only
– Separate from cause-and-effect
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The Normal Distribution
• An important model to describe variability
– Most commonly encountered continuous
random variable is the normal random variable
whose values are distributed according to a
bell-shaped curve (normal curve)
– 68% of population lies within 1 SD of the mean
• 95% of population lies within 2 SD of the mean
• 99.7% of population lies within 3 SD of the mean
• Central limit theorem
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Random Sampling
• The process of selecting members from the
population is called sampling from a
• Selected elements represent a sample
• Number of elements is referred as sample
size (n)
• Random sample: each possible sample has
the same change to be selected
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Things to Watch When
Displaying Information
• Cutting off the bottoms of a bar chart
– Bottom trick
• Using a wrong display of area
– Dimensional effect
• Use of symbols can be misleading
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