02-Basic%20Statistics%20Review%20-%20class

02-Basic%20Statistics%20Review%20-%20class - Basic...

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Unformatted text preview: Basic Statistics Review Types of Data Basic Statistics REVIEW William C. Hurst ATTRIBUTE ATTRIBUTE VARIABLE VARIABLE FDST 4090/6090 (2010) FDST 4090/6090 © W.C. Hurst 2010 Population Population vs. Sample Population Population (N) – Sample Sample (n) – subgroup or subset of a population Number Number of Central Central Tendency X (x-bar) - mathematical center point in a group of (xvalues n X= Number Number of Σ xi 3,1,5,10,16 35 = =7 5 5 i =1 n FDST 4090/6090 © W.C. Hurst 2010 Central Tendency (cont) (mo) (mo) – most common number in data set Sample: Sample: 1, 3, 7, 4, 7, 8, 7, 2 = FDST 4090/6090 © W.C. Hurst 2010 Measure of Dispersion Variability Variability 1. 2. ~ ( x ) – middle value in ranked numerical order of data 3. Sample: Sample: 1, 3, 10, 16, 5 = 1, 3, 5, 10, 16 FDST 4090/6090 © W.C. Hurst 2010 UGA FDST 4090/6090 - (c) W.C. Hurst 2010 FDST 4090/6090 © W.C. Hurst 2010 1 Basic Statistics Review Variance (s2) Range (R) Range Range ( R ) = n Σ ( xi − X ) 2 Sample: Sample: 3, 5, 10, 1, 16 s 2 = i =1 R = 16-1 = 15 16- n −1 FDST 4090/6090 © W.C. Hurst 2010 Standard Deviation Sample: Sample: 3, 5, 1, 16, 10 X=7 n=5 s= Frequency Distribution n s= Σ ( xi − X ) 2 i =1 n −1 (3 − 7) + (5 − 7) + (1 − 7) + (16 − 1) + (10 − 7) 5 −1 2 2 2 FDST 4090/6090 © W.C. Hurst 2010 2 2 s = 6.04 Suppose a QC technician was asked by the QA manager to determine the mean weight and variability of carrot stick packages coming off the end of a production line. After removing and weighing 30 packages, the following results were obtained. Calculate the mean, range and mean, standard standard deviation of this data set. xi Fi (frequency) 23g 11 24g 6 25g 5 26g 8 TOTAL SEE WORKSHEET FDST 4090/6090 © W.C. Hurst 2010 Sources of Variation FDST 4090/6090 © W.C. Hurst 2010 Categories Categories of Variation No two things exactly alike! FDST 4090/6090 © W.C. Hurst 2010 UGA FDST 4090/6090 - (c) W.C. Hurst 2010 FDST 4090/6090 © W.C. Hurst 2010 2 Basic Statistics Review Types of variation Common Common cause Random, Random, natural, due to chance Special Special cause (unnatural) Assignable Assignable cause Management must change process to improve OnOn-line personnel must find and eliminate FDST 4090/6090 © W.C. Hurst 2010 UGA FDST 4090/6090 - (c) W.C. Hurst 2010 Examples Examples of Variability COMMON CAUSE Slight variance in Slight variance in machine machine SPECIAL CAUSE Faulty machine set-up Faulty machine set FDST 4090/6090 © W.C. Hurst 2010 3 SECTION 2 - BASIC STATISTICS REVIEW WORKSHEETS Frequency Distribution Suppose a QC technician was asked by the QA manager to determine the mean weight and variability of carrot stick packages coming off the end of a production line. After removing and weighing 30 packages, the following results were obtained. Calculate the mean, range and standard deviation of this data set. Xi Fi (Frequency) 23 grams 11 24 grams 6 25 grams 5 26 grams 8 TOTAL 30 FDST 4090/6090 Food Quality Control g © W.C. Hurst 2010 x & MR Charts Worksheet: Page 1 ...
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