# How To Calculate The Mean

Enlarge

## How To Calculate The Mean

This video from the winner of National Lecture Competition in 1989 helps us to easily calculate the mean for a list of data, for a table of ungrouped data and for a table of grouped data.

Hi, I am Dr.Shah. I was the National Lecture Competition winner in 1989, and I am the math master at Mathscool.

Now, ready for a new way of doing maths? So just that we are working with the median, we have three different kinds of cases to consider. Case 1, we have a list of data. So the list of data might be like this data here and this might be the data for the number of times that a group of students visited the cinema last month.

So there is our data. The mean is called 'x-bar' and is found by adding together all the values of 'x' and then divided by 'n'. That 'sigma x', means that you will have to add up all the values of x.

So if you add up all these values of x, you should get forty, and divided by n(one, two, three, four, five, six, seven, eight), forty divided by eight. That gives you five at being the mean. Case 2 will be a table of ungrouped data.

So, in this case, we have got poker players taken by a tournament and these are the number of wins, twelve people did not get any win, twenty seven people managed to get one win, twenty five people got two wins and so on. So to find the mean for this data, what we are going to do first of all is that we are going to add in a new row. If I call these 'x' and I call these 'f', then my new row is going to be called 'xf' and is done by multiplying these two together.

So, no times twelve is zero, one times twenty seven is twenty seven, two times twenty five is fifty, three times thirteen is thirty nine and four times eight is thirty two. Once you have done that, we are going to total up the frequencies. So adding up all of these frequencies, maybe just in the calculator, will give you an answer of seventy nine and I am going to call that 'n'.

So n equals to seventy nine. I am going to add up these and adding up all of these again on the calculator, gives you a total of 124, the sum of all the x's. Then now, to find my mean, I do the same formula as last time, sigma x over n, except that this time my 'sigma x' is over here, one hundred and twenty four and my 'n' is here, seventy nine.

Again sticking it into the calculator, you get a mean of 1.57. The mean for a set of data, even if the data is discrete like this, the number of wins, the mean does not have to be a whole number.

It can be 1.57. It is useful to know that the mean is not one and it is not two, it is 1.

57. So that means we know that a lot of people got one win and a lot of people got two wins and the average was not exactly in between them and is slightly closer to two than it is to one. Our last case is a table of group data and that would often happen because our data is not discrete, it is continuous.

Here we have an example, we have got age: no to ten and two people in that category, ten to twenty and four people in that category and so on. Now, we are going to find the mean of this data. Now, when we have group data, you will not be able to identify the mean exactly anymore and the reason is because, of these four people that were in the ten to twenty class, we do not know, were they all ten years or one of them fifteen, one of them eighteen, one of them nineteen and the other eleven.

So because we do not know, because they have summarized the data, what we are going to be able to do is estimate the mean and this is how we do it. First thing we need to do, is to change these to the mid-values. Now we can change these to the mid-values straight away because you can see that there is no gap between the end of that class and the start of the next class.

If there is a gap, then we must first of all rewrite using class boundaries, but in this case, there is no gap so it is fine. So we are going to find the middle of each class. The middle of that class, no to ten would be five, the middle of that class would be fifteen, and the middle of that class would be twenty-five, thirty-five and forty-five.

Now that we have done that, we are going to treat it just in the sam