mode median mean

Mode, Median and Mean are terms used in statistics to describe  as simply as possible a set of data or measurements. They are often confused with each other, or just not understood correctly. However, Mode, Median and Mean are easy concepts to understand and use.

Statistics are playing and increasingly important role in everyday life. Switch on the TV, or read a newspaper, and there will be at least one report that quotes some statistical number - one in five companies are currently this; the majority of people are that. You cannot get away from stats, as they are used to sway your opinion about major issues.

But we also use stats ourselves, perhaps without even realising, and this is where knowing how to use mode, median and mean really helps. It can help describe groups of objects and people, or how much to buy of something, or what we think the weather will be like this weekend.

Lets start with the first of these, and perhaps the most simple - the Mode. The best way to show what the mode is, is to use an example. Here, we use a dice, but it could be anything.

Role a dice 10 times and make a note of the values. You could have got the numbers : 2 5 3 1 4 6 2 5 4 2 . Now, the mode is simply the most common value - simple as that! Look at the table below -

When we roles the dice, the number 2 came up most often. So, in this case, 2 is the mode. You should note right away, that this is not the mean or the average for this set of numbers. If we role the dice again, we may well get a different mode - perhaps 1 will be most often.

But what if we get two or three numbers coming up with the same equal most count? Simple, then we have 2 (or 3) modes to the set of numbers.

What if all the numbers come up only once (or all come up the same number of time each)? This is a special case where we do not have a mode. This can happen when we do not have a big set of data to use - perhaps we only rolled the dice four times, and got different numbers each time.

The second useful statistic measure is the Median. This is simply the 'middle' value of our numbers. To show how we do this, lets roll the dice again, this time we will do it 11 times.

Suppose we got 2 6 1 4 2 5 1 6 3 5 6. Now, we rewrite these numbers in order from lowest to highest - 1 1 2 2 3 4 5 5 6 6 6. As we have 11 numbers, we know the middle number will be the 6th one along. In this case the median is 4.

Before when we rolled the dice ten times to find the mode, there is no single value we to pick as the middle. So how do we work the median out for an even number? First we do exactly the same - rewrite the numbers in numerical order. So we have 1 2 2 2 3 4 4 5 5 6. Here we do not have a single middle number, in stead we have as the middle 3 and 4. The median is then just the middle of these numbers - 3 1/2.

A set of numbers can have only one median value.

You don't often hear the word mean being used in this sense, but it is the same as average. The mean can be considered as the best single value to describe a set of numbers. It is also the one that can take longest to calculate.

We have rolled our dice twice already, so lets use what we have to demonstrate working out the mean. In our first example we had 2 5 3 1 4 6 2 5 4 2. We need to add these numbers up, and then divide by the number we have. So :

Total = 2 + 5 + 3 + 1 + 4 + 6 + 2 + 5 + 4 + 2 = 34

mean = 34 / 10 = 3.4

So, the mean (or average) value for rolling our dice was 3.4. This should feel about right for a fair dice - all the numbers have an equal chance of coming up, and the mean is about half way between the maximum and minimum values.

Now lets do the same for our second set of dice rolls. Again, we add up the values we got

Total = 2 + 6 + 1 + 4 + 2 + 5 + 1 + 6 + 3 + 5 + 6 = 41

mean = 41 / 11 = 3.7

The mean of 3.7 is almost in the middle, so we can believe the dice is fair (although to be sure we would have to roll the dice many more times). But this does demonstrate that even though we used the same dice, and rolled it just one more time than before, we got a different mean value. We have to expect this when we roll dice, take measurements or canvas people's opinions, as results can vary from one time to another. And this raises an important point - the mean value can be useless if you do not have enough data to start with. How much you need is very complicated to work out, and gets to the heart of what statistics is about, but common sense will help in every day examples. If you have a large change in the mean value, with just a few extra measurements, then you will need many more measurements before the mean will be useful.