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 is taken and the absorbency on each piece was measured. The following are the absorbency values:
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.
We are given
The mean is
If we arrange the data from least to greatest, the 10th and 11th data are 20.5 and 20.72. The median therefore is
If we removed the 10% from the bottom and 10% from the top of the data arranged from least to greatest, the 4 values will be eliminated. The values eliminated are 18.04, 18.71, 23, and 23.71. Therefore, the sum of the remaining data is
The trimmed mean is
A dotplot is shown below