Document 1: Fuel Efficiency Data from Consumer Watchdog Group
A new automobile is produced with an advertised fuel efficiency of 29 miles per gallon (mpg). A consumer watchdog group
decided to field test a sample of 12 of these vehicles under similar driving conditions to verify whether this advertised
rating seems reasonable. After 5,000 miles of driving, the fuel efficiency data (in mpg) gathered from the 12 vehicles is given
Document 2: Consumer Watchdog Group’s Major Concern
The summary statistics from our data include a mean of 28.625 mpg, a median of 27.85 mpg, and standard deviation 2.82 mpg.
Our statistical concern about the mean and median differing (by nearly one mpg) is that the higher mean reflects the dominance
in the data of one or two vehicles with much higher fuel efficiency than expected.
Document 3: Statistical Testing on Mean and Median
To analyze the distribution of data, two statistical computations are available.
The S-statistic is calculated this way: S = mean / median
The R-statistic is calculated this way: R = (median – minimum) / (maximum – median)
The following S-statistic dotplot illustrates 100 examples of previous field testing by this consumer group on other samples
of 12 vehicles. For instance, one earlier field test of 12 vehicles of a different type ended up with S = 0.972. The consumer
group typically expresses public concern about the accuracy of a manufacturer’s fuel efficiency claim if S ends up one of the
10% of the highest or 10% of the lowest values of S by comparison with other field tests.
Consider each of the following statements. Does the information in the three sources support the inference as stated?
Half of all vehicles had fuel efficiency greater than the sample mean.
In general, S will have a greater value than R for data, like this set, in which there are a small number of vehicles with much higher fuel efficiency than the others.
If you take the vehicle with the highest fuel efficiency out of this data set, S decreases by more than 5%.
The high S statistic (based on all 12 vehicles) gives serious reason to be concerned that the manufacturer’s stated fuel efficiency of 29 mpg may be incorrect.