For the above example, the mean (8.492) for these data is larger than the median (8.05). This indicates that the data are skewed to the right that is, there are more extreme measurements in the right tail of the distribution than in the left tail.

Q:As a result of government and co summer pressure, automobile manufacture in the United States are deeply involved in research to improve their products gasoline mileage. One manufacture, hoping to achieve 40 miles per gallon on one of its compact models, measured the mileage obtained by 36 test versions of the model with the following results (rounded to the nearest mile for convenience):

433541424238404141404041

42 36 43 40 38 40 38 45 39 41 42 37

40 40 44 39 40 37 39 41 39 41 37 40

The mean and standard deviation of these data are shown in the SAS printout at the bottom of page 74.

A. Find the mean and standard deviation and give the units in which they are expressed.

B. If the manufacturer would be satisfied with a (population) mean of 40 miles per gallon, how would it react to the above test data?

C. Applying Chybyshevs rule and Empirical rule, check the reasonableness of the calculated standard deviation s = 2.2.

D. Construct a relative frequency histogram of the data set. Is the data set mound-shaped?

E. What percentage of the measurement would you except to find within the intervals , 2 , 3

F. Count the number of measurements that actually fall within the intervals of part E. Express each interval count as a percentage of the total number of measurements. Compare these result with your answer to part E.

2.70

2.71

2.72