7. Losen, Cahoy, and Lewis purchased eight spanner bushings of a particular type

Question

7. Losen, Cahoy, and Lewis purchased eight spanner bushings of a particular type from a local machine shop and measured a number of characteristics of these bushings, including their outside diameters. Each of the eight outside diameters was measured Chapter 3 Elementary Descriptive Statistics 116 once by each of two student technicians, with the following results (the units are inches): 2 3 4 Bushing Student A Student B Bushing 3690 3690 3690 3700 3690 3695 3695 3695 5 6 7 8 Student A .3695 3700 3695 .3690o Student B .3695 .3700 3700 3690 A common device when dealing with paired data like these is to analyze the differences. Subtracting B measurements from A measurements gives the following eight values: 0000,.0005,.0005, .0005, .0000,.0000 0005, .0000 (a) Find the first and third quartiles for these dif- (b) Find the sample mean and standard deviation (c) Your mean in part (b) should be negative. Inter- ferences, and their median for the differences pret this in terms of the original measurement problem

Explanation / Answer

(a) first quartile = -0.0005, third quartile = 0.0000, median = 0.0000.
We had to sort the data first. Then, median = average of the 4th and 5th values, first quartile = 2nd value, third quartile = 6th value.

(b) mean = - 0.000125, standard deviation = 0.00035.

(c) The mean has come out to be -0.000125 inches. This means that, on an average, the outside diameters measured by Student B were found out to be 0.000125 inches more than those measured by Student A.

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