STATISTICS-AVERAGES

Many people have a problem in interpreting statistics. This short article may hopefully help rather than hopelessly confuse you.

There is no such thing as an average business. 50% of them will be above average – and 50% will be below average. And any specific business may be far above or far below average.

The term average can refer to mean, median or mode. What do these words mean?

The MEAN is the arithmetic average value of a set of numbers. To find it you add up the numbers and divide by the total of numbers there are in the set.

 The MEDIAN is the number in the middle of a set of numbers. There are an equal number of numbers above it and below it. To find the median you have to arrange the numbers in order from the lowest to the highest, then find the number exactly in the middle. If there is an even number of items in the set there will be no middle number, so we average the two middle numbers to find the median.

The MODE is the number that occurs most often in a set of numbers. A set of numbers can have more than one mode.  In some sets of numbers there is no number that occurs more than once, and there is no mode for that set. In some sets of numbers maybe two numbers will occur at an equal but greater frequency than any other number. In this case there are two modes, and the distribution is said to be bi-modal.

Example (A)       [3            5              5              6              10           12           15]

The mean is 8                    The median is 6                 The mode is 5

Example (B)        [4            5              5              5              8              12           86]

The mean is 18                  The median is 5                 The mode is 5

Example (C)                        [80          90           90           100         84           90]

The mean is 89                  The median is 90              The mode is 90

The RANGE is the difference between the highest and lowest value. In this last example the highest value is 100 and the lowest is 80, so the range is 20

The mean average can be very misleading. If I tell you the mean income of businesses in my town is  $1 Million dollars a year, you may assume that they are all successful. But maybe most of them may have very small incomes, and there is one business that makes several million a year. The average will be large because of that one very large business.

The median and mean together give a better idea of the spread of numbers. If there was just one very large business the median income would be quite low.

The mode may also help to correct false impressions if you know the mean and the median but you don’t actually have access to examine the actual data. For example:  if I tell you I am thinking of four numbers. Their mean is 50 and the median is 50. You would probably think these four numbers are close to one another. But I am actually thinking of           100         98                1              1.

The mean is 50 and the median is 50. But the mode is 1. If you know that, you will know that 1 is repeated more than once in the data, and since the mean is 50 with only 4 numbers you will conclude that the data must also include several high numbers.

Why am I writing this? Business brokers use arithmetic means of business sales figures as a “representative value” for valuation purposes. If you average the sales price of 100 businesses the arithmetic mean would be an indicator of the average sales price. But the mean is not always the best representative value to choose. It is usually better to use the median rather than the mean.

Another method used to smooth out the anomalies in the data is to just eliminate the upper and lower 10% or 25% of the data from consideration. This will get us closer to the central tendency of the data. But it won’t help in valuing a specific business that might belong in the higher or lower decile or quartile of the value range.

We believe the specific business under consideration should be analyzed and valued on its own. It should not be compared to average figures based on other businesses that may be in the same industry but otherwise are not comparable.