Prob & Stat for Engr 1 class notes 1/5/15
Prob & Stat for Engr 1 class notes 1/5/15 ENGR 0020: Probability and statistics for Engineers I
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This 3 page One Day of Notes was uploaded by Emily Binakonsky on Saturday January 10, 2015. The One Day of Notes belongs to ENGR 0020: Probability and statistics for Engineers I at University of Pittsburgh taught by Maryam Mofrad in Spring2015. Since its upload, it has received 203 views. For similar materials see Probability and Statistics for Engineers 1 in Engineering and Tech at University of Pittsburgh.
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Date Created: 01/10/15
ENGR 0020 Probability and Statistics for Engineers I Emily Binakonsky Instructor Maryam Mofrad 1515 ENGR 0020 Probability and Statistics for Engineers I Instructor Maryam Mofrad Office Hrs Tu 12145 Benedum 1230 Class Notes 1 Introduction to Statistics and Data Analysis a Objectives i Statistical Inference samples populations and role of probability ii Sampling procedures collection of data iii The Sample Mean and the Median iv Measures of Variability v Statistical Modeling scientific inspection and graphical diagnostics b Statistics are used to make judgments and decisions when there is uncertainty 2 Variability in Scientific Data a Ex In manufacturing one can encounter differences in the material from product to product from different batches of product to within the product batches 3 Populations amp Samples It s important to collect the sample data in a systematic way to reduce bias How it works PopulationgtProbabilitygtSamplegtStatistical Inferencegt Population a Population All individuals of individual items of a particular type b Sample Normally a subset of the population is a subset of measurements selected from the population of interest c Census collected data on entire population d The role of probability It bridges descriptive and inferential statistics It explains the uncertainty associated with the sample e Descriptive Statistics summarize and describe important features of the sample data Also organizes the data f Inferential Statistics Techniques for drawing conclusions about the population based on information obtained from the sample Also analyzes and interprets the data and make decisions 4 Sampling Data Collection if not collected properly data cannot be analyzed with a high degree of certainty it also may not be representative of the population One could use the entire population choose a simple random sample stratified sample or design an experiment a Sampling Methods 1 Simple Random sample n items and each is equally likely to be selected 2 Systematic Random sample take evey mth item 3 Convenience Sample a sample population selected because it is readily available convenient 4 Stratified Sample subpopulation stratum take proportionally equal items from m different groups ENGR 0020 Probability and Statistics for Engineers I Emily Binakonsky Instructor Maryam Mofrad 1515 5 Experimental Design a In an ideal experiment we would randomly assign subjects to each treatment group i Flipped teaching vs Traditional teaching b Ex Determine whether coating an aluminum metal with corrosion retardation substance reduced the amount of corrosion seen Tab I2 D i r l39 Example I3 verr gg urru i u in knitting Hirlnrriietglilzy Thnu hndlaer ul7 I31g39alllt39H Plat IEiir th a 2U Illltzuil l t cl r Hill 35 nite l F5 Chijuiced fftil39l ll allf l quot Etl i b HELEN 6 Notation a n Number of observations in a sample sample size b N Number of elements in the population in finite c X1 X2 Xn individual observations 7 Measures of Location a Sample Mean x is an estimate of the population mean u It is the center of the sample as it relates to location If 11I1xn I E 039 T1 11 Population Mean u c Median xquot represents the middle value in the data where onehalf the data is above and onehalf the data is below when the data is ordered from lowest to highest i How to find the median when 1 n is odd order the data the data point in the middle is the median 2 n is even order the data sum the two middle data points and divide by two ii The population median is depicted as uquot d Mode is the data point that occurs most often You can have more than one mode e Trimmed Mean Described as the compromise between the mean and the median For example when finding a 10 trimmed mean it would be computed by eliminating the smallest 10 and the largest 10 of the sample data and finding the mean of what is left This pretty much eliminates the effect of outliers on the data i An m percent trimmed mean is denoted by x mm f Quartiles amp Percentiles g Sample Proportions 8 Measure of Variability a Range Range largest value smallest value Whenthe range is large the variability is high The limitation of this measure is that it only focuses on the most extreme values b Variance is deviation from the mean 1 Steps a Subtract x from each of the n sample observations ENGR 0020 Probability and Statistics for Engineers I Emily Binakonsky Instructor Maryam Mofrad 1515 b Square each of the altered observations c Add all the squared altered observations together d Then divide that sum by quotnl 2 Sample variance 532 If i i1 Iii 1 2 N Kielt J 39 Eg1T 3 Population variance c Standard Deviation i Sample Standard Deviation 3 as 1 Steps a Take the square root of the sample variance and you have the sample standard deviation ii Population Standard Deviation J E m 1 Steps a Take the square root of the population variance and you have the population standard deviation