# What is an Average?

How many times do you hear a report in the media and it refers to an average?

How many times have you used the word Average?

How many times do you hear others referring to an average?

Averages are something that we use in mathematics, school, economics, production, sales, marketing and numerous other places…… Whether we talk about Average Wage, Average Income per capita or referring to a norm, we tend to use the term average without much thought….. Are you aware that the there is more than one average?

Though a statistician or a mathematician will tell you that there are many definitions for Average I am going to keep it simple and go through three methods to calculate an average. If you look up average in a dictionary you will see a definition such as

*“A number that typifies a set of numbers of which it is a function”*

In layman talk we consider an average to be about the middle (ie a set of numbers) or the normal (ie the average Australian….).

However when dealing with numbers I am going to go through three methods of calculating an average:

- Mean
- Mode
- Medium

The Mean is the most common way that average is calculated. The Mean is adding up the numbers and then dividing them by the number of numbers. This number will be the Mean.

The Mode is the number that appears the most in the set of numbers.

The Medium is the middle number. The Medium is calculated by lining up the numbers in ascending order and then picking out the middle number.

**For Example:**

- Number series: 0, 1, 1, 2, 4, 5, 5, 5, 6
- The Mean is 3.22 (The numbers added together and then divided by 9)
- The Mode is 5 (number that appears most often)
- The Medium is 4 (the number in the middle)

As you can see from the example each of the methods for calculating the Average gives a different answer. There are advantages and disadvantages to each of the methods and they suit different purposes. This I may cover in a future blog. However I hope this has you thinking that next time you hear the word Average…. Stop and think about how they calculated the average and what this means.

Posted on Monday, 17 Sep 2012, in Uncategorized and tagged Average, Business, Calculation, Commerce, Economics, Integers, Invest, Investing, Investment, Math, Mathematician, Mathematics, Maths, Mean, Medium, Mode, Mode (statistics), National average salary, Number, Number Theory, Numbers, Recreations, Sales, School, Specific Numbers, Statistician, Statistics. Bookmark the permalink. 13 Comments.

Thanks for the informative post. Now I have a question for you, since you’re into stats. 🙂

I read a little news item years ago about an artist in Egypt who was searching for wife #50. He’d been married 49 other times and I suppose in his Muslim country men can “collect” wives — or maybe he said “I divorce thee; I divorce thee; I divorce thee” to the other 49.

Anyway, if you took a survey of 50 men, him and 49 others married once each, what would the divorce “statistic” be for that group of men?

It sometimes seems we get blown away by statistics on this and that –our media loves to do that– when it actually could be 90% normal people and 10% who’ve really tipped the scales.

Christine,

You pose a very good question. And this is where you need to be careful and not take statistics on face value. In your example the Medium=1, Mode=1 and mean=nearly 2. Very big difference in the average…… As you would be aware there is other tools like Standard deviation that can shed light on Statistics. However, I think that most people view statistics as a set thing, when it is not. I once heard a saying that sums up statistics….. “There are lies, there are dam lies and then there are statistics”.

Cheers

Attila

Thanks for the refresher Attila. Another good measure is standard deviation, helping to understand the ‘spread’ or distribution of the numbers or samples. Once folks realise what a standard deviation is telling them, its a great tool (in addition to the average) to help understand what you are dealing with.

Standard deviation is also a good measure for looking into the risk or volatility of an investment. Of course there is many uses. Thank you for the comment

So, if I’m an average day, then I’m actually have a “mean” day?? LOL

I would hope not…. lol…. However I do wish your a fantastic day….

What’s up with the math lesson today? 🙂 You know I am working in an accounting department and I still don’t like math. I know that does not seem quite right, does it? 🙂

All good…. As long as you can do the maths, does not mean you have to like it….

Good of you to post this. I went through the definitions in my head to make sure I had them right; it never hurts to refresh one’s memory . . .

A very clear explanation – congratulations

Thank you for the great insight on averages Attila, have a great day 🙂

My Pleasure Tina…..

thanks for that mathematical reminder 🙂 I didn’t like statistics in school. It was becoming too complicated for me. Now I just stick to the basics…my political marketing stints can’t do without them.