Question

The accounts manager of a large retail store is investigating the number of days that customers take to pay their invoices, the normal period being 30 days. An inspection of the payment records of 30 randomly- selected customers, revealed the following payment pattern. 35 42 34 27 32 30 24 33 27 36 30 38 26 32 28 28 39 23 17 20 31 29 30 24 25 29 31 30 19 34 1.1 Using 7 classes, each of width 4, construct a frequency distribution of the above data. Let 18 be the upper limit of the initial class. 1.2 Using the grouped data determined in 1.1 above, estimate each of the following. 1.2.1 middle quartile. 1.2.2 70th percentile 1.2.3 mode. 1.3 Calculate the coefficient of variation and interpret the result.

Answer 1

1.1 Frequency distributions Range 14-18 18-22 22-26 26-30 30-34 34-38 38-42 Total Frequency Cumulative frequency 1 1 2' 3 5 8 10 18 7' 25 3 28 2 30 30 1.2.1 Median = Middle quartile Q2 = 30 * 0.5 = 15th value This will fall in range 27-30 lower band upper band 26 30 lower frequency upper frequency 8 18 (Q2 - 26)/(15-8) (30-26)/(18-8) Q2-26 Q2 2.8 28.8

1.2.2 70th percentile P70 = 30*0.7 = 21th value This will fall in range 31-34 lower band upper band 30 34 lower frequency upper frequency 18 25 (P70-30)/(21-18) (34-30)/(25-18) P70-31 P70 1.71 31.71 1.2.2 Mode Mode = L + [(f1-fo)/(2f1-f0-f2)] *H f1 fo f2 h Lower limit of modal class freqeuency of modal class freqeuency of class preceeding the modal class frequency of class suceeding the modal class Class size 10 Maximum freqeuncy Modal class 26-30 L h f1 fo f2 26 4 10 5 7 Mode 28.5

1.2.2 Coefficient of variation a = C.I Fi Xi 16 20 24 Fidi^2 9 8 14-18 18-22 22-26 26-30 30-34 34-38 38-42 1 2 5 10 7 3 2 28 di = (Xi -a)/h Fidi -3 -3 -2 -4 -1 -5 0 0 1 7 2 6 3 6 28 32 36 40 5 0 7 12 18 59 30 7 Standard deviation (S.D) 14.75 3.06 11.6875 3.42 13.67 Square root of 11.687 S.D Variance 187.00 Mean = a+h. (sum of Fidi/sum of Fi) 28.93 Coefficient of variatior S.D/Mean * 100 47.263114

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