1. Example 3.1 Measures of Central Location

2. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 SALARY.XLS n Lists starting salaries for 190 graduates from an undergraduate school of business. n The data is in the range named Salary on a sheet called Data.

3. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 The Mean n We calculate the mean salary by entering the formula “=AVERAGE(Salary)” in cell B6 of the Excel Functions worksheet. n The mean salary is $29,762. n The mean in this example is a “representative” measure because the distribution of salaries is nearly symmetric. n The mean can be misleading due to skewness.

4. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 The Median n The median is the “middle” observation when the data are listed from smallest to largest. n If there is an odd number of observations, the median is the middle observation. n If there is an even number of observations, we take the median to be the average of the two middle observations.

5. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 The Median -- continued n We calculate the median salary in Example 3.1 by entering the formula “=MEDIAN(Salary)” in cell B7 of the Excel Functions worksheet. n The median in this example is $29,850. n In this case, the mean and the median values are nearly the same because the distribution is approximately symmetric.

6. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 The Median -- continued n If the salary distribution were skewed (for example, a few graduates received abnormally large salaries), the mean would be biased upward while the median would not be affected by the unusual values. n Thus, it is better to use the median in characterizing the center of a distribution when that distribution is skewed.

7. 3.23.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.113.33.43.53.63.73.83.93.103.11 The Mode n The mode is the most frequently occurring value. n If the values are essentially continuous, as with the salaries in Example 3.1, then the mode is essentially irrelevant. There is typically no single value that occurs more than once. n Thus, the mode is not likely to provide much information.