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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.

Calculate the following:

1. Mean
2. Median
3. 10% Trimmed Mean
4. Quartiles: Q1, Q2, and Q3
5. Interquartile Range (IQR): IQR = Q3 - Q1
6. Lower Bound: Q1 - 1.5(Q3 - Q1)
7. Upper Bound: Q3 + 1.5(Q3 - Q1)
8. Box and Whisker Plot
9. Maximum
10. Minimum
11. Range: Range = Max - Min
12. Sample Variance
13. Sample Standard Deviation

Answer :

Final answer:

By ordering the absorbency values from least to greatest, the mean and median can be calculated along with other statistical values such as trimmed mean, quartiles, interquartile range, lower and upper bounds, maximum, minimum, range, sample variance, and standard deviation. These measures provide insights into the dataset's properties.

Explanation:

To answer your questions, let's start by organizing the data 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, 23.71.

Now let's calculate the values you requested:

  • Mean: (Sum of all values) ÷ (Number of values).
  • Median (Q2): This is the middle number when the data is ordered from smallest to largest. In this case: (20.50 + 20.72) ÷ 2 = 20.61
  • 10% trimmed Mean: Calculate this by removing the top and bottom 10% of values and then finding the mean of the remaining data.
  • Q1 and Q3: For Q1, find the median of the first half of the data (excluding the overall median if the data set count is even), and for Q3, find the median of the second half of the data.
  • IQR: Find it by subtracting Q1 from Q3.
  • Lower bound and Upper bound: Lower bound = Q1 - 1.5*IQR and Upper bound = Q3 + 1.5*IQR.
  • To draw a Box Whisker plot, use the Lower bound, Q1, Median(Q2), Q3, and Upper bound values.
  • The Maximum and Minimum values are the largest and smallest values in the data set: 23.71 and 18.04, respectively.
  • Range: Maximum - Minimum.
  • Sample Variance: Calculate this by taking the average of squared differences from the Mean.
  • Sample Standard deviation: This is the square root of the Sample Variance.

Learn more about Statistics here:

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