Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.8408 1374 1872 8879 2459 11413 3653608 14138 6452 1850 2818 1356 579410498 7478 4019 4341 739 2127 8305(a) Provide a five-number summary.(b) Compute the lower and upper limits.(c) Do the data contain any outliers?(d) Draw a box plot and identify the outlier(s).
Question
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.8408 1374 1872 8879 2459 11413 3653608 14138 6452 1850 2818 1356 579410498 7478 4019 4341 739 2127 8305(a) Provide a five-number summary.(b) Compute the lower and upper limits.(c) Do the data contain any outliers?(d) Draw a box plot and identify the outlier(s).
Solution
To answer your question, we first need to organize the data in ascending order:
739, 1356, 1374, 1850, 1872, 2127, 2459, 2818, 3653, 4019, 4341, 608, 6452, 7478, 8305, 8408, 8879, 10498, 11413, 14138, 3608
(a) Five-number summary:
- Minimum: 608
- First quartile (Q1): 1872
- Median (Q2): 4341
- Third quartile (Q3): 8408
- Maximum: 14138
(b) Lower and upper limits:
- Lower limit: Q1 - 1.5*(Q3-Q1) = -7794
- Upper limit: Q3 + 1.5*(Q3-Q1) = 18074
(c) Outliers: An outlier is a data point that falls outside the lower and upper limits. In this case, there are no outliers as all the data points fall within the lower and upper limits.
(d) For the box plot, you would typically use a software or online tool to generate it. The box plot would show the five-number summary and any outliers (if they existed). In this case, since there are no outliers, all the data points would be within the box and whiskers of the plot.
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