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Chapter 4: Problem 53

The San Luis Obispo Telegram-Tribune (November 29,1995 ) reported the values of the mean and median salary for major league baseball players for \(1995 .\) The values reported were \(\$ 1,110,766\) and \(\$ 275,000\). a. Which of the two given values do you think is the mean and which is the median? Explain your reasoning. b. The reported mean was computed using the salaries of all major league players in \(1995 .\) For the 1995 salaries, is the reported mean the population mean \(\mu\) or the sample mean \(\bar{x}\) ? Explain.

Short Answer

Expert verified
a. The mean salary is \$1,110,766 and the median salary is \$275,000. b. The reported mean is the population mean as it has considered all the major league players' salaries in 1995.

Step by step solution

01

Mean vs Median

The mean is the average of all the numbers, calculated by adding them all up and then dividing by the count of numbers. The median is the middle point of data when arranged in ascending order. If the data is skewed, i.e., if there are very high values (outliers), those values can greatly influence the mean, making it much higher than the median. Therefore, given that \$1,110,766 is significantly larger than \$275,000, it is safe to assume that the \$1,110,766 represents the mean and \$275,000 represents the median of the salaries.
02

Population Mean vs Sample Mean

A population is a complete set of items being studied. Here, as the mean salary was calculated using all major league players' salaries in 1995, the reported mean is a population mean (\mu), not a sample mean (\bar{x}). A sample mean would be if the mean was calculated from a subset or a part of all major league players' salaries in 1995.

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