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

Tasks:
(a) Calculate the sample mean and median for the above sample values.
(b) Compute the 10% trimmed mean.
(c) Create 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?

Question

24-03-2024
Mathematics

High School

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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

Tasks:
(a) Calculate the sample mean and median for the above sample values.
(b) Compute the 10% trimmed mean.
(c) Create 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 :

Final answer:

This question involves calculating the sample mean, median, and trimmed mean for a series of absorbency measurements, creating a dot plot using this data, and discussing potential evidence of outliers using these findings.

Explanation:

To start, we'll need to organize these absorbency measurements in ascending order: 18.04, 18.71, 18.92, 19.25, 19.29, 19.44, 19.77, 20.17, 20.33, 20.50, 20.72, 21.12, 21.41, 21.77, 21.81, 22.11, 22.43, 22.85, 23.00, and 23.71.

(a) To calculate the sample mean, add up all these values and divide by 20 (the total number of samples). To get the median, find the average of the 10th and 11th values (20.5 and 20.72).

(b) The 10% trimmed mean requires cutting off the top 10% and bottom 10% of the data, which means removing two values from each end. The remaining mean of the 16 values will give the trimmed mean.

(c) A dot plot can be drawn by placing each value on a horizontal number line and placing a dot for each occurrence of that number.

(d) The mean, median, and trimmed mean are all measures of central tendency. If these values are significantly different, it might suggest the presence of outliers. However, without more information about the overall distribution of the data, it's hard to make an ironclad determination about outliers simply based on these three metrics.

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Answer :

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