## Mean vs. median: What do they mean and when do you use them?

Should you use median income or average income statistics to get a more accurate projection of what is occurring in our communities?

Should you use median income or average income statistics? Cubit’s Blog suggests the answer is to use median income data -- either instead of or in addition to – average income data, because outlier data can skew the average.  An outlier is a value that "lies outside" most of the other values in a set of data and is much smaller or larger than in value.

It is important to understand the difference between average (mean) income and median income. The average (mean) income is the sum of a set of numbers divided by the count of numbers in the data set. To determine the average, add up all the numbers in the data set and then divide by how many numbers there are in the data set.

Median income is the middle number in the data set, which can be determined by placing all the numbers in value order and finding the middle number in the data set. If there are two middle numbers, then take the average of the two middle numbers to obtain your median income.

So why would you use one over the other? It all comes down to the possibility of an outlier number skewing the result to be less representative of the “average” number.

Statistics for the Terrified discusses using symmetry to determine if the mean or median should be used in data analysis:

The mean is calculated by adding together all the values, and then dividing them by the number of values you have. As long as the data is symmetrically distributed (that is, if when you plot them on a frequency chart you get a nice symmetrical shape) this is fine - but the mean can still be thrown right out by a few extreme values, and if the data is not symmetrical (ie. skewed) it can be downright misleading.

The median, on the other hand, really is the middle value. 50 percent of values are above it, and 50 percent below it. So when the data is not symmetrical, this is the form of “average” that gives a better idea of any general tendency in the data.

So remember: Always use the median when the distribution is skewed. You can use either the mean or the median when the population is symmetrical, because then they will give almost identical results.

Those in Michigan State University Extension that focus on land use provide various training programs on planning and zoning, which are available to be presented in your county.  Contact your local land use educator for more information.