Variance and standard deviation (grouped data)

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Variance and standard deviation (grouped data) IntroductionIn this leaflet we extend the definitions of Variance and standard deviation to data which has a set of values, which we denote by 2,isdefined as 2= f(x x)2nwhere xis the mean,xstands for each data value in turn, andfis the frequency with which datavalue,x,occurs. Note that f= alternative, yet equivalent formula, which is often easier to use is 2= fx2n x2where x= fxn(The Mean)Worked exampleFind an estimate of the Variance and standard deviation of the following data for the marks obtainedin a test by 88 (x)0 x<1010 x<2020 x<3030 x<4040 x<50Frequency (f)616242517Wecan show the calculations in a table as follows:MarksMid Intervalffxx2fx2Value (x)0 x<1056302515010 x<2015162402253 60020 x<30252460062515 00030 x<4035258751 2

Standard deviation = √ 138.727 =11.78 Exercises Find an estimate of the standard deviation of the following: 1. a) Lifetime Frequency b) Income Frequency c) House Frequency (hours) of (1000’s £) prices components (1000’s £) 300 ≤ l<400 13 10 ≤ i<15 9 40 ≤ p<60 5 400 ≤ l<500 25 15 ≤ i<20 16 60 ≤ p<80 9 500 ≤ l<600 66 20 ≤ ...

  Standards, Deviation, And standard deviation, Standard deviation