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Q1 According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber was taken and the absorbency on each piece was measured. The following are the absorbency values: 18.71 21.41 20.72 21.81 19.29 22.43 20.17 23.71 19.44 20.50 18.92 20.33 23.00 22.85 19.25 21.77 22.11 19.77 18.04 21.12 Calculate: Sample Mean . Sample Median 10% trimmed Mean Quartiles: Qi, Q2 and Q3 Interquartile range: IQR Q3-Q . Lower bound = Q1-1.5(Q3-Q1) e Upper bound - Qs 1.5(Qs-Q1) . Box Whisker plot e Maximum . Minimum . Range = Max-Min Sample Variance . Sample Standard deviation
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pieces(x)x-X bair (x-X bar)A2 acsending order 18.71 21.41 20.72 21.81 19.29 22.43 20.17 23.71 19.44 20.5 18.92 20.33 23 22.85 19.25 21.77 22.11 19.77 18.04 21.12 415.35 2.05 0.65 0.04 1.05 1.47 1.67 0.59 2.95 1.32 0.26 1.84 0.43 2.24 2.09 1.51 1.01 1.35 0.99 2.72 0.36 4.2025 0.4225 0.0016 1.1025 2.1609 2.7889 0.3481 8.7025 1.7424 0.0676 3.3856 0.1849 5.0176 4.3681 2.2801 1.0201 1.8225 0.9801 7.3984 0.1296 48.1265 18.04 18.71 18.92 19.25 19.29 19.44 19.77 20.17 20.33 20.5 20.72 21.12 21.41 21.77 21.81 22.11 22.43 22.85 23 23.71 1) Sample mean = X=425/20 x= 20.762) Sample median (n+1)/2 -21/2 10.5 Sample median 10th obs 11th obs /2 Sample median (20.5+20.72)/2 Sample median 20.61 10% trimmed mean: 10/100-0.1 3) G-floor(trimmed mean percent *sample size) G floor(0.1*20) G- 2 Trim the first and last two valuesAnd find mean of remaining values Trimmed mean 331.89/16 Trimmed mean 20.743 4) Quartiles Q1- (n+1)th obs/4 21/4 (5.25)th obs - 5th obs - 0.25(6th obs - 5th obs) - 19.29 - 0.25(19.44-19.29) Q1 19.25 Q2- median 20.61 Q3 3(n+1) /4 - 3(21)/4 (15.75)th bos Q3 15th obs - 0.75 (16th obs -15th obs) -21.81 -0.75(22.11 - 21.81) Q321.58 5) Interquartile range Q3 Q1 21.58 19.25 Interquartile range- 2.33 6) Lower boundQ1-1.5( Q3- Q1) - 19.25 -1.5(2.33) Lower bound 15.7557) Upper bound Q3 +1.5 (03-Q1) 21.58 1.5(2.33) Upper bound 25.075 8) Maximum=23.71 9) Minimum 18.04 10) Range max min Rsnge- 23.71-18.4 Range= 5.67 11) Sample variance=E(X-Xbar)^2 n-1 -48.1265/19 Sample variance S2.5329 12) Sample standard deviation - S- V2.532913) Sample standard deviation S-1.5915 14) Box whisker plot Series2 Series4 10 15 20 25 0

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