## What is a “mean”?

In simple terms, it is the average of a series of numbers. Mean is a term used widely in statistics, even more than in accounting and personal finance.

## How is it calculated?

If there are three numbers in a series – say 4, 9 and 11, the mean is calculated by adding them and dividing the sum by the number of digits. So the mean of 4, 9 and 11 is:

(4+9+11)/3 = 24/3 = 8

More generally, the formula for the Mean may be written as:

Mean = Sum of the numbers / Count of the numbers

## Examples in the context of accounting

We don’t often talk about “a mean” in accounting. We are more likely to say “average”. We might be interested in the average cost of something – for example, if a business bought 100 widgets at £2 per widget yesterday and today bought another 50 widgets at £2 each, on average, the business has spent £150 on widgets per day.

How did we work that out? The sum of the cost incurred on the first day is £200 and the cost incurred on the second day £100 divided by the number of days (or spending events), which is 2.

(£200+£100)/2= £150

Note that the sum is expressed in £ (the sum of spending amounts), whereas the denominator is a count number (has no £ sign in front of it). The result (average spend per day or the mean) is expressed with a £ sign because it is a cost, not a count number.

Another example might be when talking about shares on the stock market. If you bought 30 shares in X Plc today for £4 each and then sometime later you bought another 50 shares at £5, then the average price of the shares you hold will be:

(30 x £4 + 50 x £5) / (30+50)

(£120 + £250) / 80

£370/80 = £4.625

In reality, we will probably round that off to £4.62 when we speak about it, even though that would not be the precise average or mean.

In summary, in accounting, means are not often spoken about, but averages (average cost, average price, average production hours, average salary, average weekly turnover, average profit, etc.) are talked about and calculated all the time. Mean and average mean the same thing.

A look in Sainsbury’s Annual Report and Financial Statements* for the year to 6 March 2021 reveals that the word “average” appears 65 times.

One example on page 65 of the report reads:

“The annual aggregate of non-audit fees is capped at 70 per cent of the annual average of the audit fees for the business for the preceding three-year period”.

What that means is that if the fees for audit in 2021 were £3.3m, in 2020: £3.9m and in 2019: £3.2m, the annual average of non-audit fees in 2022 will be capped at 70 per cent of (£3.3m + £3.9m + £3.2m)/3

= £10.4m/3

= £3.37m

The word “mean” appears only five times in the same report in relation to mean ethnicity pay gap, mean gender pay gap and mean black pay gap as part of the company Ethnicity and Gender Pay Gap reporting.

The mean (or average pay) for all male employees is calculated by adding all-male employees’ salaries and dividing by the number of male employees. The mean (or average pay) for all female employees is calculated by adding all-female employees’ wages and dividing by the number of female employees. The gap between those two means is then reported.

It is curious that the number of times the words “average” and “mean” have been used are very different. It confirms that in accounting, we just simply like to call the average “the average”. “The mean” is more of a statistical term reserved perhaps for statistics textbooks and reports.

## Examples in the context of personal finance

Similar to accounting, in the context of personal finance, we refer to “average” more often than the “mean”, and we mean the same thing. The Financial Times has several articles which refer to “average pay” or “average cost” or “average price”.

You can probably easily relate to scenarios from your financial circumstances. E.g., if you are a student who has a part-time job and in the first week of December you earned £200 in wages, £250 in the second week, £270 in the third and busy pre-Christmas week but only £100 in the fourth week when the holidays are upon us, then on average you have earned:

(£200 + £250 + £270 + £100)/4 = £820/4 = £205 per week

But we are used to saying “average pay” rather than “mean pay” a lot more even though they are the same thing.

The method of calculating the mean pay is just the same in this context as in accounting or statistics or any other context:

*Mean = Sum of the numbers / Count of the numbers*

You may be paying, say, £40 for electricity in August, but £80 in December when it is cold and dark, and electricity is used more. On average (or the mean cost), you are paying is

(£40 + £80 )/2 = £60.

Of course, to be more precise about that statement, the cost of the other months of the year would need to be included in the sum and that electricity cost sum divided by 12, the number of months in a year. Or you may be babysitting for one family and charge them £20 per hour, but for another family, with more kids, you charge more, say £25 per hour. On average (or the mean price of your babysitting services) is then:

(£20 + £25)/2 = £22.50.

The application of the mean or average calculation is, as you can see, universal.