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The following table lists the 2009 total profits (rounded to millions of dollars) of the seven Fortune 500 companies in the Computers, Office Equipment category (Source: www.money.cnn.com/magazines/ fortune/fortune500/2010/industries/8/index.html). \begin{tabular}{lc} \hline & 2009 Profit \\ Company & (millions of dollars) \\ \hline Hewlett-Packard & 7660 \\ Dell & 1433 \\ Apple & 5704 \\ Xerox & 485 \\ Sun Microsystems & \(-2234\) \\ Pitney Bowes & 423 \\ NCR & \(-33\) \\ \hline \end{tabular} Find the mean and median for these data. (Note: The negative values for Sun Microsystems and NCR imply that both companies lost money in 2009.) Assume that these seven companies constitute the population of such companies in the 2009 Fortune 500 .

Step by step solution

01

Calculate Mean

Firstly, add all the profits from each company, including the losses (negative profits): \(7660 + 1433 + 5704 + 485 - 2234 + 423 - 33\). Then, divide this sum by the number of companies (7) to get the mean profit.

02

Calculate Median

In order to calculate the median, the profits should be arranged in ascending order: \(-2234, -33, 423, 485, 1433, 5704, 7660\). As there are 7 companies, the median is the fourth value, which is 485.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Mean

Mean is one of the most commonly used measures of central tendency in descriptive statistics. It is essentially the "average" of a data set and gives you an idea of the overall "center" of the data.

• To calculate the mean, you add up all the values in the dataset.
• Then, you divide this total by the number of values you added.

For example, if you have a list of numbers, such as profits and losses listed by different companies, adding these together gives a cumulative figure. By dividing this sum by the number of companies, we obtain the mean profit.
In our example with the seven Fortune 500 companies, this process gives us insight into the average profitability of these companies, despite some having losses.

Exploring Median

The median represents the middle value of a dataset when it is ordered in ascending or descending order. Unlike the mean, it is not affected by extremely high or low values, making it a robust measure of central tendency.

• First, arrange the data from smallest to largest.
• If the number of observations, n, is odd, the median is the middle number.
• If n is even, average the two middle numbers.

In our example, the dataset is arranged with profits and losses, from \(-2234\) to \(7660\). Since there are seven companies (an odd number), the median profit is the fourth data point, which is \(485\) million dollars.

Introduction to Statistical Analysis

Statistical analysis involves collecting and examining data to uncover patterns and trends. It uses descriptive statistics like the mean and median to summarize and interpret data.

• The mean provides a general "center" by calculating an average.
• The median offers insight into the dataset's central tendency without skew from outliers.
• Outliers, such as very high or low profits, can distort the mean but not the median.

Through statistical analysis, we not only find these central tendencies but also explore variability within the data and make informed conclusions, such as understanding the economic standing of each company in our given dataset.

Understanding Population Data

Population data refers to the complete set of data points that you're studying within a certain context. In statistics, a population includes all elements you're interested in analyzing.

• The population can refer to people, companies, or entities within a specific domain.
• Knowing the entire population enables precise statistical analysis without the need for inference.
• The calculations for the mean and median in a population provide exact measures of central tendency.

In the Fortune 500 companies example, we assumed these seven companies constituted the entire population in the Computers, Office Equipment category for 2009. This means our analysis was based on complete data, allowing for direct conclusions about this business sector's profitability.