## Fortune Global 500

The Fortune Global 500 is a list of the largest 500 companies worldwide ranked by revenue. The list is compiled and published annually by Fortune magazine. In the 2011 list for Fortune Global 500, the top company is Wal-Mart Stores, which tops the list two years in a row. The revenue for Wal-Mart Stores is $421,849 millions (or$421.849 billions). The next three positions are Royal Dutch Shell ($378.152 billions), Exxon Mobil ($354.674 billions) and BP ($308.928 billions). The smallest company on the list is Bristol-Myers Squibb ($19.484 billions).

There are 500 data points for revenues in Fortune Global 500. What are some of the ways we can summarize the data. Since the data are already sorted, it is convenient to use measures of position to summarize the data. For example, we can use the first quartile, the second quartile (median) and the third quartile, in addition to minimum and maximum (these 5 numerical summaries together are called the 5-number summary).

One important thing to keep in mind is that the median of a data list is the middle data element (when the data values are sorted). If the size of the data list is an odd integer, then the median is the middle data value. If the size of the data list is an even integer, then there is no middle data value and the median is obtained by taking the average of the middle two data values.

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Rules to keep in mind:

When the size of the data list is $n$ (an odd integer), the position of the middle value is:

$\displaystyle (1) \ \ \ \ \ \ \ \ \ \ \frac{n+1}{2}$

When the size of the data list is $n$ (an even integer), the positions of the middle two values are:

$\displaystyle (2) \ \ \ \ \ \ \ \ \ \ \frac{n}{2} \text{ and } \frac{n}{2}+1$

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For example, in Fortune Global 500, the middle two companies would be the 250th and 251st on the list. They are Centrica ($35,547.6 millions) and Sunoco ($35,453 millions). The average revenue of these two companies is $35,500.3 millions ($35.5 billions). Thus the median company on the Global 500 list is about 8.4% of the top company Wal-Mart Stores.

The median is a numerical summary that is a measure of position, meaning that it is determined by ranking the data. The median is the middle data value when the data values are ranked from smallest to largest (or from largest to smallest as in Fortune Global 500). Since the median is the middle value, 50% of the data are below the median and the remaining 50% of the data are above the median.

In most introductory statistics courses, numerical summaries such as mean, median, and statdard deviation are usually calculated using technology (for example, a graphing calculator such as TI83 plus). In the case of median, on occasions it actually makes more sense calculating median using the definition. This is especially true when the data are already sorted as in the case of Fortune Global 500. You surely do not want to punch in 500 revenue data values into TI83 plus. If the data are already presented as sorted, just locate the middle data (or the middle two data values).

Another interesting exercise is to find the 5-number summary of the revenues in Fortune Global 500. The 5-mumber summary of a data list consists of: minimum, first quartile (Q1), median, third quartile (Q3), maximum. The first quartile is the 25th percentile (a numerical value separating the bottom 25% of the data from the top 75% of the data). The third quartile is the 75th percentile of the data (a numerical value separating the bottom 75% of the data from the top 25% of the data).

When the data are already sorted, the first quartile is simply the median of the data values less than the median. Likewise, the third quartile is simply the median of the data values greater than the median.

The 5-number summary for the revenues of Fortune Global 500 is:

$. \ \ \ \ \ \ \ \ \ \ 19,484 \ \ \ 25,889.25 \ \ \ 35,500.3 \ \ \ 60,694.7 \ \ \ 421,849$

This is left as exercise for the interested readers. The numbers in the 5-number summary are in \$ millions.

Question
Based on the 5-number summary, what is the shape of the data distribution of the revenues in Fortune Global 500?