Something approximating a normal distribution means that most of the values are clustered around the middle. When you have a distribution like this, taking the mean, median, or mode of your data all makes sense because most values would be clustered around the mean. Here is an image of what a normal distribution looks like.

A skewed distribution is when most values cluster toward the left or toward the right rather than in the center. An example of what a skewed distribution is here (scroll down to “Histograms” to see what they look like in Histogram charts).

If highly skewed, the mean is often not that valuable of a measure, especially the greater the spread (i.e., meaning there are really high or low outliers). Outliers can increase or decrease the value of the mean in ways that do not capture what might make more sense as a “common” value. Thus, in this case, it might be best to use the median or mode.

So, for instance, say you had two distributions, one normal and one skewed.

The normal would look like this: 1, 2, 2, 2, 3

The skewed would look like this: 1, 2, 2, 2, 47

The median and mean for the normal would be 2. The median for the skewed distribution would be 2 and the mean would be 10.8. Would the mean or median work better for the skewed distribution?

A uniform distribution means that there really isn’t much of a common value because there is equal spread throughout the range of values. Therefore, doing a measure of central tendency might not be very meaningful. See the image at the bottom of this webpage.

The same is true for a bimodal distribution that is highly polarized. A bimodal distribution is when there is not much of a center of the data and it is “skewed” on both sides of the distribution about equally. Like a uniform distribution, it probably isn’t very meaningful to take the mean or median. This has some good examples of what bimodal distributions look like.

Unlike uniform distributions, though, you can take the mean/median/mode of two groups you can form from the bimodal distribution to compare. So you get the “typical” value of the one pole and the “typical” value of the other pole.

To see the distribution of your numeric data with Excel, click here.

 

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