Exercise 3.51 (Algorithmic)} Annual sales, in millions of dollars, for 21 pharma
ID: 3068938 • Letter: E
Question
Exercise 3.51 (Algorithmic)}
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
Provide a five-number summary.
Compute the lower and upper limits.
Do the data contain any outliers?
SelectYes, the data contain outliersNo, the data do not contain outliers
Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?
SelectYes, a transposition would have produced an outlier, and a review would have found itNo, a transposition would have produced an outlier but a review would not have found itNo, a transposition would not have produced an outlier
Explanation / Answer
The data arranged in ascending order is
591 ,717, 1315, 1333, 1795, 1817, 2063, 2385, 2733,3543 ,3899, 4211, 5620, 6258, 7254, 8057, 8156, 8613, 10183, 11071, 14138
a) Five Number Summary
Minimum: 591
First Quartile : Q1 = (n+1)/4 = 5.5th value
Q1 = (1795+1817)/2 =1806
Median = (n+1)/2 = 11th value
Median = 3899
Third Quartile : Q3 = 3(n+1)/4 = 16.5th value
Q3= (8057+ 8156)/2 = 8106.5
Maximum = 14138
b) Inter Quartile Range (IQR) = Q3-Q1 = 8106.5- 1806 =6300.5
Lower Limit = Q1 - 1.5*IQR = 1806-1.5*6300.5 =-7644.75
Upper Limit =Q3+1.5IQR = 8106.5+1.5IQR = 17557.25
c) Do the data contain any outliers?
Answer: No, the data do not contain outliers
d) Answer: Yes, a transposition would have produced an outlier, and a review would have found it, because the other values like Q1, Q3 and IQR does not affceted by the maximum value.
Which of the following box plots accurately displays the data set?
Answer: Data set 3) is correct
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