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.