Public transportation and the automobile are two alternatives an employee can use to get to work each day. Samples of times recorded for each alternative are shown below. Times are in minutes.Public transportation: 28 29 32 37 33 25 29 32 41 34Automobile: 29 31 33 32 34 30 31 32 35 33 A. Compute the sample mean for both alternatives.B. Compute the sample standard deviation for both alternatives.C. Based on your results from part (a) and (b), which alternative should be preferred?
Question
Public transportation and the automobile are two alternatives an employee can use to get to work each day. Samples of times recorded for each alternative are shown below. Times are in minutes.Public transportation: 28 29 32 37 33 25 29 32 41 34Automobile: 29 31 33 32 34 30 31 32 35 33 A. Compute the sample mean for both alternatives.B. Compute the sample standard deviation for both alternatives.C. Based on your results from part (a) and (b), which alternative should be preferred?
Solution
A. To compute the sample mean for both alternatives, you add up all the times and divide by the number of samples.
For public transportation: (28+29+32+37+33+25+29+32+41+34) / 10 = 32 minutes
For automobile: (29+31+33+32+34+30+31+32+35+33) / 10 = 32 minutes
B. To compute the sample standard deviation, you first find the variance (the average of the squared differences from the mean), and then take the square root of that.
For public transportation: Variance = [(28-32)^2 + (29-32)^2 + (32-32)^2 + (37-32)^2 + (33-32)^2 + (25-32)^2 + (29-32)^2 + (32-32)^2 + (41-32)^2 + (34-32)^2] / 10 = 16.4 Standard deviation = sqrt(16.4) = 4.05 minutes
For automobile: Variance = [(29-32)^2 + (31-32)^2 + (33-32)^2 + (32-32)^2 + (34-32)^2 + (30-32)^2 + (31-32)^2 + (32-32)^2 + (35-32)^2 + (33-32)^2] / 10 = 2.4 Standard deviation = sqrt(2.4) = 1.55 minutes
C. Based on the results from part (a) and (b), the automobile should be preferred. Although the mean travel time is the same for both alternatives, the standard deviation (which measures variability) is lower for the automobile. This means that travel times for the automobile are more consistent and less likely to vary greatly from the mean.
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