# Statistics: How to find mean of bins

1. Sep 11, 2010

### Niles

1. The problem statement, all variables and given/known data
Hi

Say I have the following bin sizes, where the number in paranthesis is the amount of data points contained in the bin:

20-29 : (2)
30-39 : (7)
40-49 : (12)
50-59 : (14)

How would I go about and find the mean for this binned data? I know that I should use

$$mean = \frac{1}{N}\sum\limits_j {n_j x_j },$$

where bin j corresponds to a value xj and contains nj elements. But in my case, what are the values of the bins?

2. Sep 11, 2010

You usually treat this as a weighted mean problem. Think this way: if you needed to select one value from inside each bin, what value (intuitively) would be the one to pick if you didn't want to over- or under-estimate typical values in the bin? That's the value you use for x.

3. Sep 11, 2010

### Niles

I would use the average value of the data samples in that particular bin. Would you also do that?

4. Sep 11, 2010

No - you need to use a number that comes from the bins, not the collected data.

5. Sep 11, 2010

### Niles

Then the average of the bin-size, i.e. for 20-29 it is 24.5?

6. Sep 11, 2010