Chapter 191 Data Analysis and Data Presentation Chapter 19 Achieving Quality Through Continual Improvement Claude W. Burrill / Johannes Ledolter Published by John Wiley & Sons, Inc., 1999 Prepared by Dr. Tomi Wahlström, University of Southern Colorado

Chapter 192 Introduction Data need to be summarized and displayed so that its meaning can be shared with all parties involved 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 193 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 194 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 195 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 196 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 197 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 198 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 199 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 1910 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 1911 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 1912 Questions?

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