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Problem 49 Hard Difficulty

The Major League Baseball team with the highest payroll in 2010 (and most other years) was the New York Yankees. The following table gives the salary of each Yankee in 2010. Source: About.com.
a. Find the mean, median, and mode of the salaries.
b. Which average best describes this data?
c. Why is there such a difference between the mean and the median?

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Video Transcript

this question shows you a table of the salaries of all the New York Yankees. It asks you first to find the mean median and mode. We know that the mean is just the sum of all the values. Oops, some of all the values over the total number. Well, we know that there are 25 data points in this table, and when we add all of them up, we get a whopping 206,000 or two under 6,333,389 total dollars in salary. When we do this division, we find that the mean salary for a New York Yankee is eight million 253,000 336. Now let's look at the mean or the median. The median, since we have 25 data points is gonna be at the position n plus 1/2. So 25 plus 1 26 divided by two equals 13. So it's gonna be at the 13th position. If we count 13 he's already in order. So if we count 13 down in our table, we get to Nick Johnson, whose salary is five million 500,000. Also, if we look at the mode, we see that that salary 5,500,000 is the only one that repeats. So that's also our mood. 5,500,000. So which which of these now is the best? Identify our central tendency, our best average? Well, it looks like medium is going to be the best. That seems to be the one that's most in the middle the most its most. Ah, it tells the most about the rest of the data. So medium is really gonna be our best average and that why are median and mean so different? Well, it's because we have a lot of extreme values. You look at Alex Rodriguez a salary. It's way off to the rights. If we made a history, Graham would be way off to the right, and that is skewing called skewing our average. So is making her average a lot higher than the median