One of the great myths of everyday folk psychology, and one especially relevant to smaller businesses with a more limited range, is the idea that most customers pay the average price for a product or service. It has a certain intuitive appeal – that’s why it’s the average because most people are paying it. The reality, as any shopkeeper or restaurant waiting team member knows, is that this doesn’t seem to happen very often in practice and the majority of customers seem to consistently be paying either more or less than the average price on a frequent basis, depending what we have on offer. Why is this and how can we manage these discrepancies ito better control margins/sales?

A quick but very basic statistics lesson, grossly over-simplified deliberately to extract the key things we need to know in order to manage prices. The average, as most people know, is more accurately known as the **mean** and it is simply the sum of a group of items, divided by the number of items. If we have three sandwiches on offer priced at £1.50, £3.50 and £4.00, then the mean price of a sandwich is £3.00. So far, so good. The mean is a measure of what is called **central tendency** and it is just one way people look for the middle-of-the-road option, albeit it’s the best known one. The reason most people *don’t* go for average-priced options very often, aside from the fact that no individual product is often to be found at that price )as in my sandwiches example) is that gravitating towards the mean requires the customer to actually work it out and, in most cases, we don’t. We simply infer what the average must be from what we see in front of us and make our (often unconscious) evaluation of what we’re willing to pay on the basis of that ‘estimated average’.

As most of my statistics students know to their cost (or boredom), there are two other common measure of central tendency. One is the **mode**, or the most common value in a set. Let’s imaging I have five brands of ketchup in stock, with prices of £1.20, £2.50, £2.50, £3.00 and £3.10. The mode here is £2.50 because there are simply more brands at that price than any other price point. Out of interest here, the mean/average price here is £2.46, slightly lower than the mode. The other measure of central tendency often cited is the **median**, or the price-in-the-middle if you like. To calculate this, we just arrange the prices in ascending order and literally look for the value in the middle; again it’s £2.50 because this is the third number among five numbers place in ascending order. Now, do either of these get us any further in understanding, and then trying to manage, which option most customers go for? No, not really, because although the mode and median at least have the advantage of being real prices people could actually go for, unlike my mythical £3.00 sandwich earlier which didn’t exist anyway, neither the mode nor the median predict what most people will go for any more reliably. So, what are we to do?

As I said earlier, the problem here is that most people don’t work out the average, they just make an assumption of what the average must be on the basis of what they see in front of them. Neither the mode nor the median seem to gives us that, at least on a consistent basis. A neglected measure of central tendency that is really exerting influence here in FMCG buying situations is the **mid-range point**. Now, I said earlier that customers don’t generally spend time calculating the average – the maths can sometimes be hard and a waste of cognitive effort to do so – but that doesn’t mean they aren’t unconsciously performing other calculations. Experiments of how people mis-calculate averages in psychology have consistently found that the mid-range is being calculated by the brain, even though most of the time we aren’t even aware of it.

The **range** in statistics is simply the difference between the most expensive item and the least expensive one. If my most expensive sandwich is £6.00 and my least expensive one is just £1.00, then the range in terms of my sandwiches is £5.00. Turns out that what most customers do without even knowing it is to base their decision on half this value, the **mid-range value** in statistical terms. In other words, if you ask a customer leaving my shop what the average price of a sandwich was, a significant majority will “guess” that it is £2.50 (half of £5.00). Sometimes this is the same as the mean, the mode or the median, often it is not. The two important things to note here are that the mid-range will be given by an overwhelming majority of my customers as their estimates of the average and, crucially, it is based on only two pieces of data – the highest price and the lowest price, all of the ones in between and the number of brands to choose from being completely irrelevant, Ok, so if we want to forecast what ‘average’ our customers are working to, then the mid-range is the best option to go for. Ah, but how do I then manage that so they go for the option I want to promote? How can I use that knowledge to promote particular products or brands?

People have an in-built tendency to simplify information and, in particular, to go for two options; high and low. This is called the **binary bias** in psychology and we can think of it as the customer unconsciously sorting brands into the “cheap ones” and the “dear ones”. They do this sorting on the basis of the mid-range and, on the whole, they will go for either the least-expensive or more-expensive cut-off point depending on the skew (or imbalance) in the number of items in that cheap/dear category.

Let’s take a simple example. Sticking with sandwiches, let us go back to my original example and imagine I have more options available; £1.00, £1.00, £1.20, £2.00, £2.25, £2.50, £3.10, £3.10, £3.10, £3.95 and a premium offer at £6.25. On the basis of the mid-range and binary bias combined. most of my customers here would actually buy the £2.50 option. Why? Because the mid-range is about £2.63 and there are more options below that mid-range (five differently priced items) than there are above it (three prices). The number of different options available at a price is irrelevant, so this is different to relying on the media, it’s the number of prices that really matters. Although there will always be customers who are the occasional exception, this works most of the time and is way more reliable a predictor of the best-selling option than any other central tendency route!

How can I use this now to promote a particular sandwich option? Suppose I want to sell more of the £3.10 sandwiches. That’s easy, just increase the mid-range value to above £3.10 and make sure I have more price options available below it than above. For instance, I might carry a very small number of super-premium sandwiches at £7.50, which would move the mid-range to £3.25. As there would still be more price options below £3.25 (a total of six now) then there were above it (a total of three including the new super-premium one), this tactic would work. Most customers would go for the £3.10 one because of our natural tendency to gravitate to the mid point and go for the category (cheap/dear) with the most “choice”.

And of course the same would work in reverse. I might want to really push that £2.25 option because, despite its price, it has the highest profit margin. An easy way to achieve that would be to do reduce my premium offer from £6.25 to £5.55 (moving my mid-range value to about £2.27) and put my £2.50 option up to £3.10 too, thus ensuring there were less price options available above £2.27 (i.e. now there’s just £3.10, £3.95 and £5.55) than there were below it (£1.00, £1.20, £2.00 and £2.25).

So there we go… the key take-aways here… Our customers don’t work on averages when deciding what to buy, just their unconscious perceptions of what they assume the average to be. The real value they gravitate towards is simply half of the mid-range. Left to their own devices, they will go for the option just above or below that point. To manage which option they go for, however, we need to exploit the binary bias too. In other words, we need to make sure that the mid-range is where we want it to be *and* that we make sure that there are more options to choose from below that mid-range value than there are above it. Simple, really 🙂