618 Chapter 16 Business Statistics
There are other measures of central tendency used in certain special situations. Some
examples include the mode (the value that occurs most often) and the midrange (the mean
of the highest and lowest values). Since the mean and median are overwhelmingly the most
commonly used, however, we will confine our discussion to those two measures.
People are often sloppy in their terminology, using the term “average” to indicate either
the mean or the median. Averages reported in the media may be either means or medians,
and it is often unclear which measure is actually being used. As the above discussion has
demonstrated, and as many of the exercises will further show, there is often a significant
difference between the two.Example 16.2.1 A cell phone manufacturer is testing the time that a new phone can
be used before the battery must be recharged. The company takes six phones, brings
them up to full charge, and then tests to see how long the charges last with the phone
in use. The times for each of the phones (in minutes) are 408, 348, 386, 420, 468, and- Find the mean and median time.
Mean ___^408 ^348 ^386 6 420 ^468 ^400 405 minutes
To fi nd the median, we put the times in order: 348, 386, 400, 408, 420, 468. Since there
is an even number of times, there is no one single value in the middle, so we take the two
middle values and fi nd their mean:Median __^400 2 408 404 minutes
In this case, the mean and median are quite close. (This often, though certainly not always,
happens.)These two different “averages” are summarized in the table below.“A verage” How to Calculate It What It Tells YouMean Add up all the values, then
divide by the number of values.The average in the usual sense
of the term. Unusually high or
unusually low values have an
impact on the mean.
Median Put the values in order, then
choose the middle value. If
there are an even number of
values, take the mean of the
two middle values.The middle value. Unusually
high or unusually low values are
thrown out, and have no impact
on the median.Weighted Averages
A weighted average is an average in which certain items are counted more heavily (i.e.,
given greater “weight” than others.)
We have seen weighted averages in many areas of this text. For example,In Chapter 6, we used them to estimate the predicted performance of an investment
portfolio (each asset’s performance was weighted according to the percentage of the
overall portfolio that it represented),
In Chapter 10, we used them to fi nd a credit card’s average daily balance (each balance
was weighted according to the number of days that it was in place).
In Chapter 15, the average cost method for inventory uses a weighted average as well.Weighted averages are very useful in business when an overall average value is needed, but
some items are considered more important to that value than others, for example, because
of their size in relation to the overall business picture.