Premier Motorcars is the new fiat dealer in Delavan, Illinois, It has been regul
ID: 3216950 • Letter: P
Question
Premier Motorcars is the new fiat dealer in Delavan, Illinois, It has been regularly advertising in its local market area that the new Fiat 500 averages 30 miles to a gallon of gas and mentions that this figure may vary with driving conditions. A local consumer group wishes to verify the advertising claim. To do so, it selects a sample of recent purchasers of the Fiat 500. It asks them to drive their cars until two tanks of gasoline have been used up and to record the mileage. The group the calculates and records the miles per gallon for each purchaser. The data in Case Exhibit 21.1-1 portray the results of the tests.
Purchaser Miles per Gallon Purchaser Miler per Gallon
1 30.9 13 27.0
2 24.5 14 26.7
3 31.2 15 31.0
4 28.7 16 23.5
5 35.1 17 29.4
6 29.0 18 26.3
7 29.8 19 27.5
8 23.1 20 28.2
9 31.0 21 28.4
10 30.2 22 29.1
11 28.4 23 21.9
12 29.3 24 30.9
Questions:
1 For the sample given in the test, compute the following values:
a. Interquartile Range (IQR): compute the IOR for the sample (Q3-Q1). Than determine if there are any outliers in the data by determining the upper and lower limits which may be computed by:
i. Upper: Q3+1.5xQ3
ii. Lower: Q1-1.5xQ1
iii. This is a form of a confidence interval. Observations that are larger than the Upper or Small than the Lower are sometimes considered outliers and removed from the analysis.
Explanation / Answer
The data given in question statement is as follows:
Sorting the above data in ascending order on the basis of Miles Per Gallon column:
Total number of observations = n = 24
Calculation for Q1:
Q1 = Lower Quartile Value = Value at 25th percentile
k = 25 x n / 100 = 25 x 24 / 100 = 6
Since, k is an integer, we take the mean of k and (k+1) values to find out Q1
Q1 = Mean of 6th and 7th values = (26.7 + 27.0) / 2 = 26.85
Calculation for Q3:
Q3 = Upper Quartile Value = Value at 75th percentile
k = 75 x n / 100 = 75 x 24 / 100 = 18
Since, k is an integer, we take the mean of k and (k+1) values to find out Q3
Q3 = Mean of 18th and 19th values = (30.2 + 30.9) / 2 = 30.55
Hence, IQR = Q3 - Q1 = 30.55 - 26.85 = 3.70
Lower Limit = Q1 - 1.5 x IQR = 26.85 - 1.5 x 3.70 = 21.30
Upper Limit = Q3 - 1.5 x IQR = 30.55 + 1.5 x 3.70 = 36.10
Based on the above limits, any value lesser than 21.30 or more than 36.10 will be considered as an outlier. Looking at the data points for miles per gallon in the table above, we can observe that there is no data point that is outside of the above limits. Therefore, there is no outlier present in the data.
Purchaser Miles Per Gallon 1 30.9 2 24.5 3 31.2 4 28.7 5 35.1 6 29.0 7 29.8 8 23.1 9 31.0 10 30.2 11 28.4 12 29.3 13 27.0 14 26.7 15 31.0 16 23.5 17 29.4 18 26.3 19 27.5 20 28.2 21 28.4 22 29.1 23 21.9 24 30.9