An article considered various issues associated with determining endotoxin conce

Question

An article considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the article.

(a)

Determine the value of the sample standard deviation for each sample. [Hint:

xi = 237.0 for the urban sample and 128.4 for the farm sample, and

xi2 = 10,079 for the urban sample and 1617.94 for the farm sample.] (Round your answers to two decimal places.)

urban-settling s = farm-settling s =

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0 F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 0.3

Explanation / Answer

Solution:
Sample standard deviation = sqrt(summation(Xi-Xbar)^2/(n-1))

Xbar for urban settled = 237/11 = 21.5454
Xbar for farm settled = 128.4/15 = 8.56
So sample standard deviation can be calculated as
= sqrt(((6-21.5454)^2 + (5-21.5454)^2 + (11-21.5454)^2 + (33-21.5454)^2 + (4-21.5454)^2 + (5-21.5454)^2 +(80-21.5454)^2 + (18-21.5454)^2 + (35-21.5454)^2 +(17-21.5454)^2 +(23-21.5454)^2)/(10)
sqrt(241.6594+273.75+11.2054+131.2078+307.84+273.75+3416.9402+12.5698+181.2626+20.6600+2.1158)/10) = 22.2996 or 22.30
Average of farm settling = 128.4/15 = 8.56
Sample standard deviation for farm settling = (sqrt(((4-8,56)^2 +(14-8.56)^2 + (11-8.56)^2 + (9-8.56)^2 +(9-8.56)^2 +(8-8.56)^2 +(4-8.56)^2 +(20-8.56)^2 +(5-8.56)^2 +(8.9-8.56)^2 +(21.8.56)^2 +(9.2-8.56)^2 +(3-8.56)^2 +(0.3-8.56)^2)/(15-1))
After solving this equation we found
Sample standard devaition of farm settling = 6.0876 or 6.09

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