How to choose bin sizes for histograms - YouTube

This is Stephanie from StatisticsHowTo.com and in this video I will be showing you how

to choose bin sizes to make a histogram. There isn't an equation to choose bins.

I have a few general rules you'll want to follow. Bins should be the same size.

You can see on this histogram here, the bins are 8 spaces apart from 118 to 126, 126 to

134 and so on. You need to include all of the data including

any outliers. Use whole numbers whenever possible.

And choose 5 to 20 bins. If you have a small data set, you are going

to want to go with 5 bins, a very large data set, 20 bins.

It is a judgment call. Let me give you an example.

Here is a list of 20 items in my data set. The first thing I need to do is find my lowest

value and my highest value. Here is my lowest value, 1.

And here is my highest value, 50.1. Now, rule 3 says we need to use whole numbers,

so I am going to round 50.1 up to 51. My bottom number is a whole number, so that

is fine. The next step is I need to decide how many

bins to use. Rule 4 says, I should use between 5 and 20

bins. I only have a small amount of items in my

data set, so I am going to go with the lowest number.

I am going to go with 5 bins and see how that works out for me.

Now remember, we need to use whole numbers. I want to find out whether my number of bins

is going to divide into my range. My range is my highest number minus my lowest

number, so 51 minus 1 is 50. And 50 is divisible by 5.

In fact, 50 divided by 5 gives me 10. And I am going to use that number to create

my bin boundaries. My bin boundaries are these numbers right

here on the ticks, 118, 126 and 134. For my data set, these are going to be a little

different. So I am going to create my bin boundaries.

I am going to want to start my histogram at 1, the lowest number.

And then I am going to add 10 to get my next bin boundary, that gives me 11.

I am going to add 10 again, 21. Then add 10 to get 31, 41, and then I am going

to stop at 51, because that has included all of my numbers.

Now of course, things are not always going to be that simple.

You are not always going to choose the right bins and you numbers might not cooperate.

Well, you can round up or round down. Let me give you another example.

Let us say I have a list of 100 numbers, which means I am going to want to have a middling

bin size probably around 10. And let us say these numbers go from 1 to

48. Well, if I subtract to find my range.

I find my range is 47. 47 is a prime number.

I am not going to be able to find any bins that are going to evenly divide into 47.

So what I would here was I would round up to 50.

And let us say my hypothetical range is 50. That way if I choose bins starting at 1.

Let us say I am going to have 10 bins. So my range 50 divided by 10 is 5.

So I am going to go up by 5 each time. So 1 plus 5 is 6.

6 plus 5 is 11. I am going to keep on adding 5.

And eventually, my last bin number will be 51.

Now, my range was 1 to 48, and I will have included all my numbers in these bins 1 through

51. Just remember, always use whole numbers.

This is very much a judgment call. If you are using a program like Excel, you

will be better able to fiddle around with bin sizes and see which ones work and which

ones do not. But that is basically how to find bins for

histograms. Visit us at StatisticsHowTo.com for more articles

and videos on elementary statistics and AP statistics.