Don't be mean, especially not average

Anyone who has taken a statistics course knows that the word mean has a different definition than what we are used to in our regular daily lexicon.  

The common definition of mean in statistics in simplistic terms is the sum of all the observations/total number of observations.  

In our everyday language, we might use the word average which can be slightly different from the mean yet for the sake of this passage, let’s say they are one and the same. 

In talking about mean or average in statistics, you might hear what is called a normal distribution or commonly known as a bell curve with the mean (average) sitting right underneath the highest point in the curve. 

The bell curve represents all the observations you are looking at, from the lowest figure to the highest figure. 

For example, let’s say you were looking at sales figures per ticket for your restaurant during the lunch period in a 5-day week.  

Your lunch specials range from $12 to $30 per meal offered in addition to the regular menu of soups, sandwiches, and salads. 

If you served 100 patrons in a 5-day period for a total sales figure of $1705, your average sales ticket would be $17.05. Good to know. 

Question. Is this good or bad? 

Let’s add a few more data points.  

Let’s say the lowest ticket that week was $9 and the highest was $29. 

How does that $17.05 average ticket sale look now? 

If that $17.05 is sitting underneath the highest point of the bell curve, look to the left what do you see? Look to the right what do you see? 

Answer. In simplistic terms, you will see 49% of the sales tickets under $17.05 going towards the lowest $9 and 49% of the sales tickets above $17.05 going towards the highest $29. 

Alright, enough math. 

The point I am trying to make is that the average of anything is one data point that is important to know, yet it is not necessarily a good place to be. 

In the case of this restaurant, the average ticket for this 5-day period is closer to the lowest ticket sale than the highest ticket sale.  

Your lunch menu prices might not be resonating with the patrons. 

Meaning, some people may have just ordered soup or a salad that was not part of the lunch special. 

If this was my restaurant, I might be disappointed with the weekly average ticket sale. Or, maybe I need to revise my lunch special menu and the prices or promote the specials in a more meaningful way. 

To give you another example.  

Imagine you were selling your house and your agent suggested to place the selling price for your home at $350K. Imagine their reasoning was that comparable houses to yours in your area and in similar condition, size and age were selling for this average. 

This means, almost half the houses are selling for less, which you might be happy about, yet almost half are selling for more. 

Is the average really where you want to be?  

However, if the average was very high, with not a great deal of distance from the lowest to the highest, that may be a different story. 

This brings us to another very important number that is often left out other than in a statistics class; the standard deviation from the mean. 

I won’t go into an extensive explanation of standard deviation yet what you need to know is that under a normal distribution bell curve, 3 standard deviations from the mean (average) gives you 99% of the total observation points.  

Almost half the points will be to the left of the mean and the other almost half to the right. 

For example, if your mean (average) is 15 and the standard deviation is 1.5. 

Then, 15 + (3 x 1.5) = 19.5 will be close to the highest observation data point. 

And, 15 - (3 x1.5) = 10.5 will be close to the lowest observation data point.

In the restaurant example, the observation data points would be each ticket sale. 

The simple question is, when faced with the average of anything, where do you want to be? 

If and when you are faced with the average of anything, ask about the standard deviation if available. 

Having this data point will give you a better idea of if the average is a good thing or maybe not. 

Personally, if someone offered me the average of anything, I might ask for average + at least 2 standard deviations from the mean. 

If I had to pay for something, I might ask to pay the average - at least 2 standard deviations from the mean.

Food for thought.