Microsoft Office Tutorials and References

In Depth Information

**Stuck in the Middle with AVERAGE, MEDIAN, and MODE**

median and the mode equal 0. The median equals 0 because that’s the middle

value in the sorted list. The mode equals 0 because that’s the highest

occurring value. As you can see, statistics prove that the new toothpaste gives 0

cavities, on average — sort of.

Look at another example. Figure 9-1 shows the results of a midterm test for a

hypothetical class. The mean, median, and mode are shown for the

distribution of grades.

Figure 9-1:

Defining

central

tendencies

in a list of

grades.

As almost always happens, the mean, the median, and the mode each return

a different number. Strictly speaking, we should say that the average grade

is 86.72, the mean value. But if the teacher or the school wants to make their

impact on students look better, they could point out that the most frequently

occurring score is 94. This is the mode and, sure enough, three students

did receive a 94. But is this the best representation of the overall results?

Probably not.

Working with the functions that return these measures of central tendencies —

AVERAGE, MEDIAN, and MODE — can make for interesting and sometimes

misleading results. Here is one more example of how these three functions

can give widely different results for the same data. Here are data for six

customers and what they spent with a company last year: