Ignore parts with eye-ball estimation & computational formula Measures of Variation Chapter 5 Homework: 1- 6 Ignore parts with eye-ball estimation & computational formula

Variation Width of distribution how much values of variable differ Independent of central tendency Measures range standard deviation variance ~

Which one do we use? Level of measure determines nominal ordinal interval/ratio

Range Simplest measure of variation depends on only 2 points of data Distance between highest & lowest value range = highest - lowest Same range, very different distributions 2, 6, 6, 6, 6, 6, 10 2, 2, 2, 6, 10, 10, 10 ~

SS s2 s SS, s2, & s Other measures of variation related sums of squares variance standard deviation All data points represented Mean Squared Deviations Formula Computational formula not covered SS s2 s

Deviation Distance of any point from mean error Sample: deviationi = Xi - X Population: deviationi = Xi - m ~

Sums of Squares (SS) Sum of squared deviations S (distance of each point from mean)2

Variance Mean of squared deviations s 2, s2 n - 1 : s2 underestimated for sample correction factor: increases s2 degrees of freedom ~

Standard Deviation Square root of variance s , s Mean deviation why use squared deviations ~

Inflection Points of Normal Distributions Point on curve where curvature changes upward to downward downward to upward normal curve: 2 inflection points no matter width ~

Inflection Points of Normal Distributions Wider distribution: inflection points farther from mean Standard deviation equals Distance from inflection point to mean normal distribution only Can obtain rough estimate avoid large mistakes ~

Inflection Points of Normal Distributions