Question

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 Mediarn 10% trimmed Mean Quartiles: Q1, Q2 and Q3 Interquartile range: IQR Q3-Q1 Lower bound-Q1-1.5(Q3-Q1) Upper boundQ3+1.5(Q3- Q1) Box Whisker plot Maximum . . Minimum . RangeMax - Min Sample Variance Sample Standard deviation

Answer 1

Let x denotes absorbency values and $\sum x=415.35$

n- number of observations=20

1) sample mean=  $\sum x/n = 20.7675$

2) Sample median= 20.61

Using MS-EXCEL function = median(number1,[number2],...)

3)10% trimmed mean= 20.7556

Using MS-EXCEL function = TRIMMEAN(array,percent)

4) Quartiles

Using MS-EXCEL function

Q1= quartile(array,1) = 19.4025

Q2= quartile(array,2) = 20.61

Q3= quartile(array,3) = 21.885

5) Interquartile range= Q3-Q1

= 21.885-19.4025

= 2.4825

6) Lower bound= Q1-1.5(Q3-Q1)

= 19.4025 - 1.5*( 21.885-19.4025)

= 15.6788

7) Upper bound= Q3+1.5(Q3-Q1)

= 21.885+ 1.5*( 21.885-19.4025)

= 25.6088

8) Maximum= 23.71

Using MS-EXCEL function = Max(number1,[number2],...)

9) Minimum= 18.04

Using MS-EXCEL function = Min(number1,[number2],...)

10) Range= Max- Min = 23.71-18.04

= 5.67

11) Sample variance= 2.5329

Using MS-EXCEL function = var(number1,[number2],...)

11) Sample Standard deviation=1.5915

Using MS-EXCEL function = stdev(number1,[number2],...)