The Daily Dongle: Mean, Median, Mode.

October 15, 2007

Mean, Median, Mode.

Many novice users call and ask us about 'mfi' of their data. Since the acronym is ambiguous, we ask the scientist to specify if they are asking about median, mean, or geometric mean fluorescence intensity.

Mean and Geometric mean are easiest to understand - here are their formulae (from wikipedia):

Mean (aka arithmetic average) is defined as the sum of N things divided by N:

If your data is scaled in Log, you might want to use the log-friendly version of Mean, the Geometric Mean. This expression takes the Nth root of the product of N things:

Median is the number which divides the first half of your data from the second half, if sorted by some variable. Suppose you had 1 event with fluorescence of "262144" and 19 events with fluorescence of "1". The "mean" fluorescence would be (262144+19)/20 = 13108.

The Median fluorescence is 1 - if we sort the events by fluorescence and divide them in two parts, half of the events will have intensity no less than 1, the other half, no more than 1.

Depending on how you look at your data, Median usually gives the representation of a "typical" event. In the example above, no single event had fluorescence of "13108" which is what Mean would have us believe!

Also here is an interesting figure demonstrating the relationship of mode/median/mean in some types of distributions.