Introduction to Summary Statistics Introduction to Engineering Design Unit 3 – Measurement and Statistics Introduction to Summary Statistics Introduction to Engineering Design © 2012 Project Lead The Way, Inc.

Introduction to Summary Statistics The collection, organizing, calculating, evaluation, and interpretation of data Statistical analysis of measurements can help verify the quality of a design or process

Introduction to Summary Statistics Central Tendency “Center” of a distribution Mean, median, mode Variation Spread of values around the center Range, standard deviation, interquartile range Distribution Summary of the frequency of values Frequency tables, histograms, normal distribution, dot plots

Introduction to Summary Statistics Mean Central Tendency The mean is the sum of the values of a set of data divided by the number of values in that data set. =μ = x i N

Introduction to Summary Statistics Mean Central Tendency =μ = x i N μ = mean value xi = individual data value x i = summation of all data values N = # of data values in the data set

Introduction to Summary Statistics Mean Central Tendency Data Set 3 7 12 17 21 21 23 27 32 36 44 Sum of the values = 243 Number of values = 11 μ = x i N 243 Mean = = = 22.09 11

Introduction to Summary Statistics A Note about Rounding in Statistics General Rule: Don’t round until the final answer If you are writing intermediate results don’t round until the end Mean – round to one more decimal place than the original data

Introduction to Summary Statistics Mean – Rounding Data Set 3 7 12 17 21 21 23 27 32 36 44 Sum of the values = 243 Number of values = 11 Reported: Mean = μ = x i N 243 Mean = = 22. 09 = 11 22.1

Introduction to Summary Statistics Mode Central Tendency Measure of central tendency The most frequently occurring value in a set of data is the mode Symbol is M Data Set: 27 17 12 7 21 44 23 3 36 32 21

Introduction to Summary Statistics Mode Central Tendency The most frequently occurring value in a set of data is the mode Data Set: 3 7 12 17 21 21 23 27 32 36 44 Mode = M = 21

Introduction to Summary Statistics Mode Central Tendency The most frequently occurring value in a set of data is the mode Unimodal: One mode Bimodal: Two modes Multimodal: More than two Modes No mode: no data value is repeated

Introduction to Summary Statistics Mode Central Tendency Determine the mode of 48, 48 63, 62, 63, 49, 58, 2, 63, 5, 60, 59, 55 Mode = 63, unimodal Determine the mode of 48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55 Mode = 63 & 59 Bimodal Determine the mode of 48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55 Mode = 63, 59, & 48 Multimodal

Introduction to Summary Statistics Mode Determine the mode of 1, 2, 4, 5, 6, 7 No mode

Median Central Tendency Introduction to Summary Statistics Median Central Tendency Measure of central tendency The median is the value that occurs in the middle of a set of data that has been arranged in numerical order Symbol is x, pronounced “x-tilde” ~

Median Central Tendency Introduction to Summary Statistics Median Central Tendency The median is the value that occurs in the middle of a set of data that has been arranged in numerical order Data Set: 27 17 12 7 21 44 23 3 36 32 21 3 7 12 17 21 21 23 27 32 36 44

Median Central Tendency Introduction to Summary Statistics Median Central Tendency A data set that contains an odd number of values always has a Median Data Set: 3 7 12 17 21 21 23 27 32 36 44

Median Central Tendency Introduction to Summary Statistics Median Central Tendency For a data set that contains an even number of values, the two middle values are averaged with the result being the Median Middle of data set Data Set: 3 7 12 17 21 21 23 27 31 32 36 44

Introduction to Summary Statistics Range Variation Measure of data variation The range is the difference between the largest and smallest values that occur in a set of data Symbol is R Data Set: 3 7 12 17 21 21 23 27 32 36 44 Range = R = maximum value – minimum value R = 44 – 3 = 41

Dot plot Distribution Create a dot plot for the data below First pick your starting value and your scale. I decided to start at 0 and scale by 5. You do not have to start with 0 or scale by 5. 3 7 12 17 21 21 23 27 31 32 36 44

Introduction to Summary Statistics Dot Plot Distribution 3 -1 -3 3 2 1 -1 -1 2 1 1 -1 -2 1 2 1 -2 -4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6