Are you average and is your average mean?

When someone asks if I'm average, I immediately wonder if they're asking about mean, median, or mode? If math isn't your thing or you're intellectually lazy, skip to the bottom data elements. Since you're still reading, I'm going to take you back to junior high or high school math class and use Merriam-Webster to define these terms:

mean = a value that is computed by dividing the sum of a set of terms by the number of terms

median = a value in an ordered set of values below and above which there is an equal number of values or which is the arithmetic mean of the two middle values if there is no one middle number

mode = the most frequent value (or values) of a set of data

For those like me who read these definitions and go "huh?", here are the terms portrayed visually:
Practically speaking, let's compute each of these with a dataset of 5 numbers: 29,1,4,1,5.
Mean
29+1+4+1+5 = 40; 40÷5 = 8
Median
The numbers in value order --> 1 1 4 5 26 ... and the middle number (or the median) = 4
Mode
With the data set 29,1,4,1,5... the most frequently occurring or repetitive number = 1

When dealing with statistics about finances and income, the press is often sloppy in their use of the term "average". While most do not use mode, many identify both median and mean as average, which is too imprecise. If you add a few zeros along with a comma or two, the numbers in my dataset could be housing prices or household incomes, and not knowing whether a number is median or mean can have a big impact on how the numbers are interpreted . Because outliers, such as the number 29 in my dataset above, can skew the calculation of mean, many cost and income-based financial statistics are computed as median so that half of all such costs (or incomes, housing prices, etc.) fall above this value and half fall below.

While statistics may not lie, liars use statistics, so know the difference between mean, median, and mode. And with that lesson, here are a few facts about average in the U.S. of A.:

Median home value = $167,500

Mean travel time to work = 25.1 (minutes)

Median age = 36.4 years

Average* household size = 2.6
Average* family size = 3.18
* - assumed to be mean, but it's not clear

ALL
Median household income = $46,242
Mean household income = $62,556

Families
Median household income = $55,832
Mean household income = $72,585

Nonfamily household
Median household income = $28,050
Mean household income = $39,741

And if you're looking for a real-life example of an outlier, Bill Gates has more wealth than the bottom 45% of American households combined.

Note: All stats are from the economic profile of the 2005 American Community Survey from the U.S. Census Bureau unless otherwise noted. This survey breaks the data down further into these other profiles: demographic, social, and housing.

[update added March 13, 2007] For a fantastic essay described as "the wisest, most humane thing ever written about cancer and statistics" read The Median Isn't the Message by Stephen Jay Gould.