Chapter 4 Measures of Spread

RMS RMS size of a list: (S) (S) square values in list (M) (M) sum squared values and divide by total # of values in list (R) (R) take square root sum of squared values RMS RMS = # of values Root Mean Square (RMS)

RMS l measures size of values in list ignoring signs l “sort of like average ignoring sign”

Profits as Percent of Net Worth for a 10 Year Period Campbell Soup General Motors AVG

Four Lists Average = 100 on all 4 lists Sample (a) 100, 110, 105, 94, 90, 101, 89, 106, 105 Sample (b) 77, 99, 50, 146, 38, 126, 132, 85, 147 Sample (c) 101.5, 101, 101, 100.5, 99, 99.5, 99, 98, Sample (d) 100, 100, 100, 100, 100, 100, 100, 100, 100

Histogram Comparison of 2 Tests

center characteristic: spread Measures of center by themselves are often inadequate in describing a list of numbers. Another important characteristic: spread

Measures of Spread 1. Range largest value - smallest value SD 2. Standard Deviation (SD) RMS size of “deviations from AVG”

Measures of Spread 1. Range largest value - smallest value SD 2. Standard Deviation (SD) RMS size of “deviations from AVG” deviation from AVG = value - AVG

Calculating the SD l Find AVG of list l Calculate deviations from AVG l Find RMS size of “deviations” (S) square deviations (M) sum the squared deviations and divide by # of observations (R) take square root

SD sum of squared “deviations from AVG” SD= # of values

SD Interpretations l SD is an “average size” of deviations from AVG. AVG l SD is the typical amount by which values in a list differ from the AVG of the list.

SD on Calculators s n SD (population) s n-1 SD (sample) the SD used in this course divide by (# of obs. - 1) in RMS formula } }

NOTE: You must show your work on HW, Exams, and Labs !

SD SD and Histograms For many data sets (bell - shaped) one Roughly 68% of the observations fall within one SD of the average. two l Roughly 95% of the observations fall within two SD’s of the average.

Histogram Comparison of 2 Tests