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Basic Statistics&Use of Minitab,Belton Group,Rex Wong,Statistics,Statistics,is the branch of science that deals with the,collection,presentation,analysis,&,interpretation,of data for the purpose of,decision-making,and,problem-solving.,Statistics is a critical skill in quality improvement as statistical techniques can be used to describe and to understand,variability,.,Variability,Variability is the result of changes in the conditions under which observations are made.,Variability can come about due to changes in,material quality,machine settings or conditions,manpower standards,methods of processing,measurement,milieu(environment),Population&Sample,Population,the entire set of measurements of interest,Sample,a subset of data from the population,Parameters,numerical measures of a population,Statistics,numerical measures of a sample,Parameter vs Statistic,Parameter Statistic,Mean,Variance,Standard Deviation,Type of data “Gappiness”,Whether there are gaps between successively observed values of a variable.,Discrete Variable,gaps exist between observations,obtained by counting,Continuous Variable,no gaps exist between observations,obtained by measuring,Statistics-Objectives,Statistics,is the branch of science that deals with the,collection,presentation,analysis,&,interpretation,of data for the purpose of,decision-making,and,problem-solving,.,Objectives of Statistics:,data reduction,Descriptive Statistics,inferential measurement,Inferential Statistics,identification of relationships,Regression,ANOVA,Statistics-Overview,Statistics,Descriptive Statistics,Inferential Statistics,Graphical Presentations,Numerical Measures,Charts,Tables,Location,Dispersion,Shape,Parameter Estimation,Hypothesis Testing,Point Estimate,Interval Estimate,Parametric Methods,Nonparametric Methods,Descriptive&Inferential Statistics,Descriptive Statistics,comprises those methods concerned with collecting and describing a set of data so as to yield meaning information,Inferential Statistics,comprises those methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data,Descriptive Statistics-Overview,Descriptive Statistics,Graphical Presentations,Numerical Measures,Charts,Tables,Dot Plot,Box Plot,Histogram,Stem&Leaf Diagram,Bar Chart,Trend Chart,Frequency Distribution,Location,Dispersion,Shape,Mean,Median,Mode,Quartiles,Range,Standard Deviation,Variance,Interquartile Range,Skewness,Kurtosis,Numerical Measures,Describes the characteristics of the data set.,Key numerical measures:,measures of location(central tendency),measures of dispersion(variation),measures of shape(distribution),Measure of Location,Mean,(will not be discussed),Median,(will not be discussed),Mode,(will not be discussed),Quartiles,Quartiles,When an ordered set of data is divided into four equal parts,the division points are called,quartiles,.,The,first,or,lower quartile,Q,1,is a value that has approximately 25%of the observations below in value.,The,second quartile,Q,2,is a value that has approximately 50%of the observations below in value.It is also called the,median,.,The,third,or,upper quartile,Q,3,is a value that has approximately 75%of the observations below in value.,Quartiles,Twenty ordered observations on the times to failure(in hours)of electrical insulation material are shown below.,204 228 252 300 324 444 624 720 816 9121176 1296 1392 1488 1512 2520 2856 3192 3528 3710,Measure of Dispersion,Range,(Will not be discussed),Variance,(Will not be discussed),Standard Deviation,(Will not be discussed),Inter-Quartile Range,Inter-quartile range,The,inter-quartile range,is another measure of dispersion.,IQR =Q,3,-Q,1,The inter-quartile range is less sensitive to extreme values in a sample than the range.,For the two samples(1,3,5,8,9 and 1,5,5,5,9),their inter-quartile ranges are 5 and 0 respectively.,Measure of Shape-Skewness,Skewness,The degree of assymmetry of a distribution around its mean is referred to as its,skewness,.,Measure of Shape-Kurtosis,Kurtosis,Kurtosis,characterizes the relative peakedness or flatness of a distribution compared to a normal(,mesokurtic,)distribution.,MiniTabs Descriptive Statistics,S,tat,B,asic Statistics,D,isplay Descriptive Statistics,produces statistics for each column of data(or subsets within a column)and displays them in the,Session Window,and optionally in a graph,the user has no control over which statistics are computed/displayed,S,tat,B,asic Statistics,S,tore Descriptive Statistics,descriptive statistics for each column(or subsets within a column)are displayed in adjacent columns within the,Worksheet,the user can select which statistics are to be computed/displayed,but has no control over the order in which they are displayed,Instructor will show you the method of using Minitab.,Graphical Presentation,Visual interpretation the the data set.,Common graphical tools to illustrate a data set:,Dot Plot,Box Plot,Histogram,Stem&Leaf Diagram,Dot Plot,The,dot plot,is useful for displa
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