Statistics Chapter 17 LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Statistics, the collection, tabulation, analysis, interpretation, and presentation of numerical data, provide a viable method of supporting or clarifying a topic under discussion LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Statistical information should illuminate the user’s understanding of the issue or problem at hand LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics A population is a collection of all possible elements, values, or items associated with a situation – A population can contain a finite number of things or it may be nearly infinite Limitations may be placed on a collection of items to define the population LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics A sample is a subset of elements or measurements taken from a population LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Descriptive or deductive statistics describe a population or complete group of data When describing a population using deductive statistics, the investigator must study each entity within the population This provides a great deal of information about the population, product, or process, but gathering the information is time-consuming • Inductive statistics deal with a limited amount of data or a representative sample of the population LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Measurement error is considered to be the difference between a value measured and the true value The error that occurs is one either of accuracy or of precision • Accuracy refers to how far from the actual or real value the measurement is • Precision is the ability to repeat a series of measurements and get the same value each time Lean Six Sigma: Process Improvement Tools and Techniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics A frequency diagram shows the number of times each of the measured values occurred when the data were collected This diagram can be created either from measurements taken from a process or from data taken from the occurrences of events LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics • To create a frequency diagram: • Collect the data Record the measurements or counts of the characteristics of interest • Count the number of times each measurement or count occurs • Construct the diagram by placing the counts or measured values on the x axis and the frequency or number of occurrences on the y axis The x axis must contain each possible measurement value from the lowest to the highest, even if a particular value does not have any corresponding measurements A bar is drawn on the diagram to depict each of the values and the number of times the value occurred in the data collected • Interpret the frequency diagram Study the diagrams you create and think about the diagram’s shape, size, and location in terms of the desired target specification Lean Six Sigma: Process Improvement Tools and Techniques Donna C. Summers © 2011 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved Statistics • Histograms – Similar to frequency diagrams • The most notable difference between the two is that on a histogram the data are grouped into cells Each cell contains a range of values LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics • To create a histogram: – Step 1: Collect the data and construct a tally sheet – Step 2: Calculate the range – Step 3: Create the cells by determining the cell intervals, midpoints, and boundaries – Step 4: Label the axes – Step 5: Post the values – Step 6: Interpret the histogram LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics • Analysis of Histograms – Shape, spread, and location are the characteristics used to describe a distribution Lean Six Sigma: Process Improvement Tools and Techniques Donna C. Summers © 2011 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved Statistics – Shape: refers to the form that the values of the measurable characteristics take on when plotted or graphed – Shape is based on the distributions symmetry, skewness, and kurtosis – Spread: the distance between the highest and lowest values – Location: Where is the distribution in relation to the target? LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Measures of Central Tendency – Mean – The mean of a series of measurements is determined by adding the values together and then dividing this sum by the total number of values – Median – The median is the value that divides an ordered series of numbers so that there is an equal number of values on either side of the center, or median, value – Mode – The mode is the most frequently occurring number in a group of values LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics Measures of Dispersion Range • The range is the difference between the highest value in a series of values or sample and the lowest value in that same series – Standard Deviation • The standard deviation shows the dispersion of the data within the distribution LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics The Central Limit Theorem – The central limit theorem states that a group of sample averages tends to be normally distributed; as the sample size n increases, this tendency toward normality improves – The central limit theorem enables conclusions to be drawn from the sample data and applied to a population Lean Six Sigma: Process Improvement Tools and Techniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved Statistics To Find the Area under the Normal Curve: Xi  X Z standard normal value s X i individual X value of interest X average s standard deviation LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC.Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved  ... information should illuminate the user’s understanding of the issue or problem at hand LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC .Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved... Normal Curve: Xi  X Z standard normal value s X i individual X value of interest X average s standard deviation LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC .Summers â2011PearsonHigherEducation,... is the ability to repeat a series of measurements and get the same value each time LeanSixSigma:ProcessImprovementToolsandTechniques DonnaC .Summers â2011PearsonHigherEducation, UpperSaddleRiver,NJ07458.AllRightsReserved