Question

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8,072 1,319 1,798 8,524 2,361 10,956 585 14,138 6,194 1,776 2,705 1,302 10,078 7,179 3,859 4,167 709 2,042 3,507 5,562 7,974 Provide a five-number summary. Smallest value First quartile Median Third quartile Largest value Compute the lower and upper limits. Lower limit Upper limit Do the data contain any 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? Which of the following box plots accurately displays the data set?

Answer 1

The five-number summary for the annual sales data of pharmaceutical companies is provided, along with the computation of lower and upper limits. The data do not contain any outliers. If a data entry error had occurred, the method of detecting outliers would identify it. The question about the box plot cannot be answered without the provided options.

Step-by-step explanation:

The five-number summary consists of the smallest value, first quartile, median, third quartile, and largest value. For the given annual sales data, the five-number summary is as follows:

1. Smallest value: 585 million dollars
2. First quartile: 2,042 million dollars
3. Median: 3,859 million dollars
4. Third quartile: 8,072 million dollars
5. Largest value: 14,138 million dollars

To compute the lower and upper limits, we use the formula:

Lower limit = Q1 - 1.5 * IQR

Upper limit = Q3 + 1.5 * IQR

where Q1 is the first quartile, Q3 is the third quartile, and IQR is the interquartile range.

Using the values from the five-number summary, we find:

Lower limit = 2,042 - 1.5 * (8,072 - 2,042) = -7,606

Upper limit = 8,072 + 1.5 * (8,072 - 2,042) = 17,720

The data do not contain any outliers as all the values fall within the lower and upper limits.

If a data entry error had been made and Johnson & Johnson's sales were entered as $41,138 million instead of $14,138 million, it would be identified as an outlier using the method of detecting outliers. The upper limit (17,720) would be significantly exceeded by the erroneous value (41,138), indicating a data entry error.

As for the box plot that accurately displays the data set, it cannot be determined without the options provided.