Question

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,

Required:
a. Calculate the sample mean and median for the above sample values.
b. Compute the 10% trimmed mean.
c. Do a dot plot of the absorbency data.
d. Using only the values of the mean, median, and trimmed mean, do you have evidence of outliers in the data?

Answer 1

Answer:

Step-by-step explanation:

a )

sample mean = sum total of given data / no of data

= 415.35 / 20 = 20.76

To calculate the median we arrange the data in ascending order and take the average of 10 th and 11 th term .

= 20.50 + 20.72 / 2

= 20.61

b ) To calculate the 10% trimmed mean , we neglect the largest 10% and smallest 10 % data and then calculate the mean . Here we neglect the first two smallest and last two greatest

(18.92 + 19.25 ..... + 22.43 + 22.85) / 16

= 20.74

c )

We can easily plot the data on number line from 17 to 24

d )

Maximum value of data set = 23.71 and minimum value is 18.04

mean is 20.76 , median is 20.61 and trimmed mean is 20.74

They are between maximum and minimum values of given data . Hence there is no outliers .