Statistics Primer

Statistics Primer: Mean, Median, Mode, and More! Introduction to the Basic Ideas of Statistics and Statistical Analysis of Data

Introduction ,[object Object],[object Object],[object Object]

Averages ,[object Object],[object Object],[object Object],[object Object]

Arithmetic Mean Average ,[object Object],[object Object],A = {1,2,3,4,3,4,5,3,5,5} n = 10 sum (  ) = 1 + 2 + 3 + 4 + 3 + 4 + 5 + 3 + 5 + 5 = 35 arithmetic mean (  ) =  / n = 35 / 10 = 3.5

Arithmetic Mean Average ,[object Object],[object Object],[object Object]

Median Average ,[object Object],A = {1,2,3,4,3,4,5,3,5,5} A (sorted) = {1,2,3,3, 3,4 ,4,5,5,5} median = (3 + 4) / 2 = 3.5

Median Average ,[object Object],[object Object],[object Object]

Mode Average ,[object Object],[object Object],[object Object],[object Object],[object Object],A = {1,2,3,4,3,4,5,3,5,5} mode = {3, 5} or none

Mode Average ,[object Object],[object Object],[object Object],[object Object],[object Object]

“Random” Distribution ,[object Object],1000 rolls of one six-sided die The FREQ Procedure Cumulative Cumulative roll Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 157 15.70 157 15.70 2 190 19.00 347 34.70 3 155 15.50 502 50.20 4 169 16.90 671 67.10 5 167 16.70 838 83.80 6 162 16.20 1000 100.00

“Normal” Distribution ,[object Object],1000 rolls of two six-sided dice The FREQ Procedure Cumulative Cumulative roll Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 2 28 2.80 28 2.80 3 61 6.10 89 8.90 4 78 7.80 167 16.70 5 105 10.50 272 27.20 6 135 13.50 407 40.70 7 167 16.70 574 57.40 8 134 13.40 708 70.80 9 118 11.80 826 82.60 10 96 9.60 922 92.20 11 52 5.20 974 97.40 12 26 2.60 1000 100.00

Distribution Measures ,[object Object],[object Object],[object Object]

Standard Deviation ,[object Object],[object Object],[object Object]

Standard Deviation 1 SD 2 SD 3 SD Mean = 7.03 SD = 2.4 mean

Skewness Left-Skewed data example EXAMPLE: Time to complete task Cannot be below zero time to completion Will not likely have larger values

Kurtosis Kurtosis example Annual Rainfall per Year in rainy plain Annual Rainfall per Year in dry desert

About the Author Paul D. McDonald is the CEO of SPIKEware, Inc. and has been a SAS programmer since 1993. Paul has an A.A. in Electrical Engineering from Cloud County Community College, a B.A. in Physics from Southwestern College, and an M.B.A. in Finance from Keller Graduate School of Management. Paul can be reached by e-mail at [email_address] . ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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