# Averages in finance, Mean, Median, Mode and Weighted Averages

Average Joe…..she was average height…..the film was average….we have lots of meanings for the term ‘average’ and a whole host of ways in which the word is used.

However, when it comes to finance, its interpretation is slightly different. Using the layperson’s understanding of an average calculation could lead to less than accurate results.

We take a look at the role of averages in finance and the different ways in which they are calculated.

Getting an ‘average’

When most people refer to something being of an ‘average’ value they are typically alluding to the term which is more correctly known as the simple average, or the arithmetic mean.

This calculation is one which most schoolchildren learn and involves adding the various values together and simply dividing them by the number of components.

For example, if you had three snakes and their lengths were 25cm, 35cm and 125cm, to get the average length you would add the values together and divide by 3:

25 + 35 + 125 = 185 divided by 3 = 62 (rounded)

In other words, the average length of the snake is 62cm. Imagine your surprise when you find one which is 125cm long!

A simple average is fine for providing a rough estimate but can be unduly influenced by particularly high or low values which distort the final result.

Geometric mean

A simple average is useful where the data is not intrinsically linked but where you need to find the mean on a series of number which are related, the geometric mean offers a more suitable solution.

To find the geometric mean of any series of numbers, you simply multiply the figures and then with the product, take the nth root (where n = the number of components multiplied).

Therefore in a series with two numbers, after multiplying you would find the square root, after three numbers you would find the cube root and so on. Financial averages often are consistent.

25 x 35 x 125 = 109375 cubed = 48 (rounded)

Therefore we can see that the much larger value of 125 has a far less erroneous effect on the outcome and allows us to judge more effectively the typical size of the snake.

In finance, a geometric mean is frequently used when considering the geometric average growth rate over a period of time.

Median

There may be times in finance when it is more appropriate to determine what the midway point in a series of numbers is; another way to prevent particularly large or small figures from unduly influencing the end result.

The median is possibly one of the easiest figures to arrive at. Firstly, you must organise your list of numbers according to size rather than simply being in a random order. Then you simply find the point which is at the middle of the list. In a series where there are an odd number of entries, the median is simply the number which has the same amount of figures on either side of it. Where there is an even number of entries, the middle pair of numbers should be added together and divided by 2 to reach the median.

A median is more appropriate for longer lists and is a way of determining the central tendencies of the series.

Mode

If finding the most commonly occurring point is what you want to achieve, although the median can provide a good idea, calculating the mode will be even more revealing.

Put simply, the mode is the number which occurs most frequently in a series. Again, like a median, it is better suited to a longer series than our three snakes.

However, if the number of snakes increased so we ended up with more which measured:

25, 30, 30, 35, 35, 35, 35, 80, 80, 125

…the mode would be 35. This tells us how big the typical snake in our sample size is. Compare this to the simple average which is 51 and the median which is also 35, and you can see how mode and median calculations are much better at providing an indication of the central and most commonly occurring point on a list.

It is worth pointing out however that median and mode values are not always identical but are often very close in value.

Weighted average

Although finding the midway point or the most commonly occurring value may be useful in some circumstances, on other occasions you may want some particular components to influence the final result to a greater extent that the other values in the list.

To do this you will need to find the weighted average. Having somebody who knows how financial averages work is important.

This works by attaching a weight – which is relative to the importance – to each number in the list. Each number is multiplied by its own weight, all the results are added up and then the final total is divided by the sum of the weights.

In finance, stock markets and indices are weighted according to the importance of the sector. This prevents random and less relevant components from having a significant effect on the outcome.

A weighted average is a useful way of including all values in the result whilst still ensuring that those which you are most interested in have the greatest bearing.

Conclusion

As you can see from the above explanation, an average in finance has anything but an average explanation! The various forms of the average are helpful in different scenarios and can help you manipulate the data at hand to ensure that you can the most revealing result possible.

Image credits: noricum and Alan Cleaver