The personnel files of all eight employees at the Pawnee location of Acme Carpet

Question

The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last six-month period they lost the following number of days due to illness: 3 1 0 0 2 11 5 3

All eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost the following number of days due to illness: 3 6 8 4 4 5 3 1

a. Calculate the range, mean and mean deviations for the Pawnee location and the Chickpee location. (Round mean and mean deviation to 2 decimal places.) Pawnee location Chickpee location Range Mean

b-1. Based on the sample data, which location has fewer lost days?

b-2. Based on the sample data, which location has less variation?

Explanation / Answer

Here for Pawnee location of seried : 3,1,0,0,2,11,5,3

mean = sum of all observations/total observations = (3+1+0+0+2+11+5+3)/8 = 25/8 =3.13

Further as its minimum value is 0 and maximum is 11, so its range = 11-0 = 11

Now for mean deviation, we get the deviation of each data from mean first as :

|3-3.13|=0.13, |1-3.31| = 2.13 , |0-3.13|=0, |0-3.13|=3.13, |2-3.13|=1.13, |11-3.13|=7.87, |5-3.13|=1.87,|3-3.13|=0.13

so its mean deviation = (0.13+2.13+3.13+3.13+ 1.13+ 7.87+ 1.87+ 0.13)/8 = 19.52/8 =2.44

so its mean deviation is 2.44.

Again for Chickpee location.

Mean =(3+6+8+4+4+5+3+1)/8= 34/8 =4.25

Again its minimum value is 1 and maximum value is 8, so its range = 8-1 = 7

and now

|3-4.25|=1.25, |6-4.25|=1.75, |8-4.25| = 3.75, |4-4.25|=0.25, |4-4.25|=0.25, |5-4.25|= 0.75, |3-4.25|=1.25,|1-4.25| =3.25

So mean deviation =(1.25+ 1.75+ 3.75+ 0.25+ 0.25+ 0.75+ 1.25+ 3.25)/8= 12.75/8 = 1.59

This is the answer of part a)

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Now as sum of all observations of first set is 3+1+0+0+2+11+5+3 = 25 and the sum of second set is 34

that means Pawnee location has fewer lost days. This is the answer of part b1.

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Now variation is calculated using the formula

variation = ( sum of square of all terms)/total terms - (Mean)^2

so the variation of first set = (3^2+1^2+0+0+2^2+11^2+5^2+3^2)/8- (3.13)^2

=(9+1+4+121+25+9)/8-9.8 = 169/8 - 9.8 = 21.125 -9.8 = 11.325

and for second set,

variation = (3^2+6^2+8^2+4^2+4^2+5^3+3^2+1^2)/8- (4.25)^2

=(9+36+64+16+16+25+9+1)/8 -18.0625

=22- 18.0625 = 4

so clearly Chickpee location has less variation.

Answer

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