Textbook Example 1

Statistics provides a common language for the "shape" or "pattern" of data. A symmetric dataset is one in which if you were to divide it into two pieces through its center, the resulting pieces would be mirror images.

When the pattern of data is symmetric, the mean (or average) will be equal to the median. When data is skewed the pattern of data is off-center. If it is skewed to the right (i.e right-skewed), higher values are more spread out than lower values in the dataset and the mean will have a larger value than the median. (See Figure 1)

                                                The effect of spreading out the higher values in a dataset, note the
                                                                difference between the mean and the median.

Please answer the following thought/reasoning questions:

Question 1: Suppose the values in a dataset are "left-skewed". In plain English, please describe a graph of left-skewed distribution of data.

Question 2: Suppose the values in a dataset is "left-skewed". What is the relationship of the mean to the median in this case? To see an example, click here

Question 3: Please provide some examples of "right-skewed", "symmetric" and "left-skewed" data that we frequently encounter in every day life. If this seems difficult, try visiting a web site such as YAHOO! News and type the words "average" and "median" (no quotes) in the search window.

Question 4: Thinking back to the 10/7/02 lecture on means and medians, if you were a professional baseball player trying to negotiate your salary, which statistic (mean or median) would you use to make your argument? Why? Suppose you were an owner of a baseball team, which statistic (mean or median) would you use during negotiations with players on their salaries? Why?