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Chapter 8 Making Sense of Data in Six Sigma and Lean. How to tell “story” from dataset? Quantitative Data. Graphical Methods Dot Plots Stem-and-Leaf Plots Frequency Tables Histograms and Performance Histograms Run Charts Time-Series Plots Numerical Methods: Descriptive Statistics.

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how to tell story from dataset quantitative data
How to tell “story” from dataset?Quantitative Data
  • Graphical Methods
    • Dot Plots
    • Stem-and-Leaf Plots
    • Frequency Tables
    • Histograms and Performance Histograms
    • Run Charts
    • Time-Series Plots
  • Numerical Methods: Descriptive Statistics
how to tell story from dataset qualitative data
How to tell “story” from dataset?Qualitative Data
  • Pie Charts
  • Bar Charts
  • Pareto Analysis with Lorenz Curve
how to tell story from dataset bivarite data
How to tell “story” from dataset?Bivarite Data
  • Graphical Methods
    • Scatter Plots
  • Numerical Methods: Correlation Coefficient
    • Pearson Coefficient
    • Spearman’s Rho ()
    • Kendall’s Tau () Rank Correlation
summarizing quantitative data dot plots
Summarizing Quantitative Data:Dot Plots
  • Dot plot is one of the most simple types of plots

Example 8.1

Minitab

Graph

Dotplot

Simple

summarizing quantitative data stem and leaf plots
Summarizing Quantitative Data:Stem-and-Leaf Plots
  • Stem-and-Leaf Plots are a method for showing the frequency with which certain classes of values occur.

i160.photobucket.com/.../treediagram.png

summarizing quantitative data frequency tables
Summarizing Quantitative Data:Frequency Tables
  • constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.
  • Absolute frequencies or relative frequencies (%)

www.sci.sdsu.edu/.../Weeks/images/Frequency.png

summarizing quantitative data histogram
Summarizing Quantitative Data: Histogram

www.statcan.gc.ca/.../ch9/images/histo1.gif

summarizing quantitative data run charts
Summarizing Quantitative Data:Run Charts
  • A line graph of data points plotted in chronological order that helps detect special causes of variation

Minitab

Graph

Time Series Plot

Simple

summarizing quantitative data time series plots
Summarizing Quantitative Data: Time-Series Plots
  • A time series plot is a graph showing a set of observations taken at different points in time and charted in a time series.

Minitab

Graph

Time Series Plot

Simple

summarizing quantitative data descriptive statistics
Summarizing Quantitative Data:Descriptive Statistics

Measures of Center

  • Sample mean
  • Population mean
  • Median: the "middle" value in the dataset
  • Mode: the value that occurs most often
summarizing quantitative data descriptive statistics1
Summarizing Quantitative Data:Descriptive Statistics

Measures of Variation

  • Range: the difference between the largest and the smallest values in the dataset
  • Sample variance
  • Sample standard deviation
  • Population variance
  • Population standard deviation
summarizing quantitative data descriptive statistics2
Summarizing Quantitative Data:Descriptive Statistics

Measures of Variation

  • Coefficient of Variation (CV)
  • Interquartile Range (IQR)
slide15

Summarizing Quantitative Data:Descriptive Statistics

  • Minimum
  • Maximum
  • Median
  • First Quartile
  • Third Quartile
  • Minitab:
  • Stat
  • Basic Statistics
  • Display Descriptive..
  • Boxplot
summarizing quantitative data descriptive statistics3
Summarizing Quantitative Data:Descriptive Statistics

Identifying Potential Outliers

  • Lower inner fence (LIF) =
  • Upper inner fence (UIF) =
  • Lower outer fence (LOF) =
  • Upper outer fence (UOF) =
  • Mild outliers: data fall between the two lower fences and between the two upper fences
  • Extreme outliers: data fall below the LOF or above the UOF
summarizing quantitative data descriptive statistics4
Summarizing Quantitative Data:Descriptive Statistics

Measures of Positions

  • Percentiles
    • Percentiles divide the dataset into 100 equal parts
    • Percentiles measure position from the bottom
    • Percentiles are most often used for determining the relative standing of an individual in a population or the rank position of the individual.
  • z scores
    • Standard normal distribution ( = 0 and  = 1)
summarizing qualitative data graphical displays
Summarizing Qualitative Data:Graphical Displays
  • Pie Chart

http://techie-teacher-wanna-be.wikispaces.com/file/view/SocialPieChart.png/96606670/SocialPieChart.png

summarizing qualitative data graphical displays1
Summarizing Qualitative Data:Graphical Displays
  • Bar Graph

www.creationfactor.net/images/graph-bar.jpg

summarizing qualitative data graphical displays2
Summarizing Qualitative Data:Graphical Displays
  • Pareto Analysis with Lorenz Curve

www.spcforexcel.com/files/images/ccpareto.gif

summarizing bivariate data scatterplot
Summarizing Bivariate Data:Scatterplot

Minitab:

Graph

Scatterplot

Simple

summarizing bivariate data correlation coefficient
Summarizing Bivariate Data:Correlation Coefficient
  • Pearson Correlation Coefficient

Minitab:

Stat

Regression

Regression

summarizing bivariate data correlation coefficient1
Summarizing Bivariate Data:Correlation Coefficient
  • Spearman’s Rho ()
    • A measure of the linear relationship between two variables.
    • It differs from Pearson\'s correlation only in that the computations are done after the numbers are converted to ranks.
    • When converting to ranks, the smallest value on X becomes a rank of 1, etc.
    • D (Difference) is calculated between the pair of ranks
summarizing bivariate data correlation coefficient3
Summarizing Bivariate Data:Correlation Coefficient
  • Kendall’s Tau ()
    • A measure of the linear relationship between two variables.
    • It differs from Pearson\'s correlation only in that the computations are done after the numbers are converted to ranks.
    • When converting to ranks, the smallest value on X becomes a rank of 1, etc.
    • P is # of pairs with both ranks higher
summarizing bivariate data correlation coefficient4
Summarizing Bivariate Data:Correlation Coefficient
  • Kendall’s Tau () Example
  • Example
summarizing multi vari data multi vari charts
Summarizing Multi-Vari Data: Multi-Vari Charts
  • Show patterns of variation from several possible causes on a single chart, or set of charts
  • Obtains a first look at the process stability over time. Can be constructed in various ways to get the “best view”.
    • Positional: variation within a part or process
    • Cyclical: variation between consecutive parts or process steps
    • Temporal: Time variability
graphical tool multi vari charts
Graphical Tool: Multi-Vari Charts

Cus. Size: 1 = small

2 = large

Product: 1 = Consumer

2 = Manuf.

Cus. Type: 1 = Gov’t

2 = Commercial

3 = Education

http://www.qimacros.com/qiwizard/multivari-chart.html

graphical tool multi vari charts1
Graphical Tool: Multi-Vari Charts

Minitab:

Stat

Quality Tools

Multi Vari Chart

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