Download Example3_1

Example 3.1
Measures of Central Location
SALARY.XLS

Lists starting salaries for 190 graduates from an
undergraduate school of business.

The data is in the range named Salary on a sheet
called Data.
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The Mean

We calculate the mean salary by entering the formula
“=AVERAGE(Salary)” in cell B6 of the Excel
Functions worksheet.

The mean salary is $29,762.

The mean in this example is a “representative”
measure because the distribution of salaries is nearly
symmetric.

The mean can be misleading due to skewness.
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The Median

The median is the “middle” observation when the
data are listed from smallest to largest.

If there is an odd number of observations, the median
is the middle observation.

If there is an even number of observations, we take
the median to be the average of the two middle
observations.
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The Median -- continued

We calculate the median salary in Example 3.1 by
entering the formula “=MEDIAN(Salary)” in cell B7 of
the Excel Functions worksheet.

The median in this example is $29,850.

In this case, the mean and the median values are
nearly the same because the distribution is
approximately symmetric.
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The Median -- continued

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.

Thus, it is better to use the median in characterizing
the center of a distribution when that distribution is
skewed.
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The Mode

The mode is the most frequently occurring value.

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.

Thus, the mode is not likely to provide much
information.
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