Averages: Is it mean to use the mean?

There’s an often-quoted anecdote about the flaw of averages which recounts the story of Lt Gilbert Daniels. In the 1950s, the U.S. airforce gave him the unenviable task of taking the physical measurements of over 4000 pilots with the aim of finding the ‘goldilocks’ set of averages that would lead to better design of fighter plane cockpits. Define the measurements of the ‘average man’ and you can design the average cockpit and most pilots will fit it.
Won’t they?
Apparently not.

“Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions.” Todd Rose

In any statistical analysis it is second nature to grab the mean average as the overview stat of choice. The ill-fitting cockpit, however, is a reminder that in many circumstances with real-world data, the mean average might not actually describe anyone or anything real.

This plays out in fundraising data all the time.
‘Could you give us the average gift from this activity, please? We want to see what people raise so we can try to make fundraising more effective next time.’

Well, the short answer is no. I can give you the mean average gift from a fundraising activity, and that information will help you forecast likely income from running such an activity again (assuming similar circumstances). It will not show you anything interesting about how people are behaving. Therefore it is unlikely you will be able to influence that fundraising behaviour in the future.

In these circumstances, rather than providing the single figure to explain a distribution, I encourage clients to look at the shape of the distribution itself. A histogram of donation amounts, or a graph of banded income will nearly always show a positive skew – a bulge at the lower monetary end and a long tail of rarer larger amounts at the upper end. Plotting amount given by number of givers looks like this:


Take the mean average and you don’t see the shape, you get a number in the middle. It doesn’t tell you that the bulge exists, where it is, and it doesn’t tell you that the larger amounts are outliers. A fundraising activity where most people give £10 could have an average gift of several hundred pounds due to a few people giving £1000, which could be hugely misleading.

Using the median (the indicator of the middle that literally points to the number half-way through the data) is less likely to be skewed by the outliers and therefore is more useful in showing a truer picture of average activity – what people are potentially capable of raising. As you can see, it’s closer to the bulge than the mean.

The mode (the indicator of the exact amount that the highest number of people gave) will show you the where that bulge is. It will often be useful to think about in terms of a psychological anchor that people are rooted to. A fundraiser can use this anchor to look at whether any of their marketing is driving people towards that anchor (by use of a prompt) or whether this is a window into a wider cultural anchor that it might be worth working with rather than against.

As with many things in the realm of insight analysis, the advice is to go into investigations with an idea of what you really want to understand. It is good to think about about what an average is telling you and what you might be able to do about it.

Are you creating a cockpit that will fit nobody? Is it better to get the measure of different people and have some different fits of cockpit, or one cockpit design that is adjustable?  In marketing terms could you be designing different messages for different audiences? Or might you design a general fundraising proposition that could be customised to different audiences?

One-size does not fit all and in some cases it fits nobody at all, whether that’s for cockpits or marketing messages. Don’t be mean – no supporter you’re talking to is merely average.

I very much recommend this article taken from Todd Rose’s book The End of Average. 

A footnote on gender:
An interesting addition to the pilot story is the what happened with an equivalent discovery of the mismatch between average body measurement and real body shape in women. Whilst the pilot finding led to acknowledgement that there was no ‘average man’ and cockpit design needed to adapt accordingly, the interpretation of the finding for women was rather different. In this case, it was the opinion of experts of the time that the average ‘ideal’ for women’s bodies was not wrong, women were. They should get in shape quick-smart.

It’s never a simple question of deriving ‘fact’ from ‘data’, it’s the interpretation of meaning that counts. To that end, it matters who’s doing the interpreting, who gets to tell the story, and who faces the consequences of conclusions.

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