Chapter 19 1

Data Analysis and Data Presentation

Chapter 19Achieving Quality Through Continual

ImprovementClaude W. Burrill / Johannes Ledolter

Published by John Wiley & Sons, Inc., 1999

Prepared by Dr. Tomi Wahlström,

University of Southern Colorado

Chapter 19 2

Introduction

• 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 observations

• Basic statistical principles must be understood by everyone in the organization

Chapter 19 3

Organizing Data-The Pareto Diagram

• The relative frequencies are displayed in the form of a bar chart, with the heights of the bars representing the frequencies of the various groups

• 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

Chapter 19 4

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

Chapter 19 5

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 magnitude

• Histogram– Range of observations divided into non-

overlapping intervals

Chapter 19 6

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

frequency

Chapter 19 7

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

Chapter 19 8

Scatter Diagrams and Correlation Coefficient

• Scatter diagrams help us in a graphical form to see how two or more variables are correlated

• Correlation coefficient is a numerical value to represent this correlation– It measures linear association only– Separate from cause-and-effect

Chapter 19 9

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

Chapter 19 10

Random Sampling• The process of selecting members from the

population is called sampling from a population

• 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

Chapter 19 11

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

Chapter 19 12

Questions?

Chapter 19 13

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