Microsoft Office Tutorials and References
In Depth Information
Stuck in the Middle with AVERAGE, MEDIAN, and MODE
Several statistical functions have been upgraded since the release of Excel
2010. Generally, a function may now have a sample and population variation;
an inclusive or exclusive (of bounding values) variation; a multiple ranges or
single range variation; or some other dual purpose variation. Some functions
in this chapter are shown in this new format.
Stuck in the Middle with AVERAGE,
MEDIAN, and MODE
Are you of average height? Do you earn an average income? Are your children
getting above-average grades? There is more than a single way to determine
the middle value from a group of values. There are actually three common
statistical functions to describe the center value from a population of values.
These are the mean, the median, and the mode.
The term population refers to all possible measurements or data points, while
the term sample refers to the measurements or data points that you actually
have. For example, if you are conducting a survey of registered voters in New
Jersey, the population is all registered voters in the state, while the sample is
those voters who actually took the survey.
Technically, the term average refers to the mean value, but in common
language average can also be used to mean the median or the mode instead of
the mean. This leads to all sorts of wonderful claims from advertisers and
anyone else who wants to make a point.
It’s important to understand the difference between these terms:
✓ Mean: The mean is a calculated value. It’s the result of summing the
values in a list or set of values and then dividing the sum by the number
of values. For example, the average of the numbers 1, 2, and 3 equals 2.
This is calculated as (1 + 2 + 3) ÷ 3 or 6 ÷ 3.
✓ Median: The median is the middle value in a sorted list of values. If
there is an odd number of items in the list, then the median is the actual
middle value. In lists with an even number of items, there is no actual
middle value. In this case, the median is the mean of the two values
in the middle. For example, the median of 1, 2, 3, 4, 5 is 3 because the
middle value is 3. The median of 1, 2, 3, 4, 5, 6 is 3.5 because the mean of
the two middle values, 3 and 4, is 3.5.
✓ Mode: The mode is the value that has the highest occurrence in a list of
values. It may not exist! In the list of values 1, 2, 3, 4, there is no mode
because each number is present the same number of times. In the list of
values 1, 2, 2, 3, 4, the mode is 2 because 2 is used twice and the other
numbers are used once.