Statistics: How to find mean of bins

[Niles]

Homework Statement

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 x_j and contains n_j elements. But in my case, what are the values of the bins?

 

[statdad]

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.

 

[Niles]

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.

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

 

[statdad]

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

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

 

[Niles]

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

 

[statdad]

Yes - it's called the midpoint of the bin.

 

[Niles]

Thanks, it is kind of you to help me.

Best wishes,
Niles.