The article “The Selection of Yeast Strains for the Production of Premium Quality South African Brandy Base Products” presents detailed information on the volatile compound composition of base wines made from each of 16 selected yeast strains. Following are the concentrations of total esters (in mg/L) in each of the wines.
The article “The Selection of Yeast Strains for the Production of Premium Quality South African Brandy Base Products” presents detailed information on the volatile compound composition of base wines made from each of 16 selected yeast strains. Following are the concentrations of total esters (in mg/L) in each of the wines.
a. Compute the mean concentration.
b. Compute the median concentration.
c. Compute the first quartile of the concentrations.
d. Compute the third quartile of the concentrations.
e. Construct a boxplot for the concentrations. What features does it reveal?
(a) The sum of the numbers 284.34, 173.01, 229.55, 312.95, 215.34, 188.72, 144.39, 172.79, 139.38, 197.8, 303.28, 256.02, 658.38, 105.14, 295.24, 170.41 is 3846.75. The mean is therefore 3846.75/16 = 240.4219.
(b) The 16 values arranged in increasing order are:
105.14,139.38,144.39,170.41,172.79,173.01,188.72,197.81,
215.34,229.55,256.02,284.34,295.24,303.28,312.95,658.38
The median is the average of the 8th and 9th numbers, which is (197.81 + 215.34)?2 = 206.575.
(c) 0.25(17) = 4.25, so the first quartile is the average of the 4th and 5th numbers, which is (170.41 + 172.79)?2 = 171.60.
(d)0.75(17) = 12.75, so the third quartile is the average of the 12th and 13th numbers, which is (284.34 + 295.24)?2 = 289.79.
(e)
The median is closer to the first quartile than to the third quartile, which indicates that the sample is skewed a bit to the right. In addition, the sample contains an outlier.
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