# How to read a histogram?

I posted the following question over on StackOverflow, and I think I am having a hard time understanding exactly how a histogram works.

I have the following set of numbers between 0 and 9:

   [1] 1 0 1 4 0 0 7 3 5 3 8 9 1 3 3 1 2 0 7 5 8 6 2 0 2 3 6 9 9 7 8 9 4 9 2 1 3
[38] 1 1 4 9 1 4 4 2 6 3 7 7 4 7 5 1 9 0 2 2 3 9 1 1 1 5 0 6 3 4 8 1 0 3 9 6 2
[75] 6 4 7 1 4 1 5 4 8 9 2 9 9 8 9 6 3 6 4 6 2 9 1 2 0 5 9 2 7 7 2 8 8 5 0 6 0
[112] 0 2 9 0 4 7 7 1 5 7 9 4 6 1 5 7 6 5 0 4 8 7 6 1 8 7 3 7 3 1 0 3 4 5 4 0 5
[149] 4 0 3 5 1 0 8 3 7 0 9 6 6 9 5 4 6 9 3 5 4 2 4 8 7 7 5 8 8 8 2 6 9 3 1 0 4
[186] 1 5 9 0 6 2 1 3 0 6 0 0 8 3 2 0 0 6 0 0 4 7 2 7 1 9 9 3 9 8 4 6 6 5 3 8 1
[223] 8 7 1 3 7 6 3 6 3 6 3 2 3 2 2 7 9 2 3 2 7 5 5 8 8 2 0 1 4 0 6 3 7 1 1 1 4
[260] 7 0 2 9 2 0 5 6 0 8 9 6 2 0 0 7 2 0 4 2 0 9 1 6 9 3 0 0 2 0 6 8 4 0 7 2 1
[297] 9 5 2 4 8 5 2 9 7 9 2 9 7 4 9 3 2 7 3 6 3 6 8 8 3 7 0 9 2 7 9 0 5 4 5 8 4
[334] 3 3 1 7 8 9 7 6 2 1 7 0 5 6 5 2 9 5 4 6 2 2 2 9 0 7 7 2 2 6 3 4 2 0 5 9 6
[371] 2 1 9 0 6 0 4 8 4 3 1 5 4 2 9 5 7 3 1 5 4 5 3 7 3 8 6 2 4 6 1 1 4 0 0 5 8
[408] 6 7 4 2 8 0 2 5 4 8 3 0 6 4 8 6 4 1 8 1 5 4 9 4 3 2 0 5 0 7 9 2 9 8 9 6 5
[445] 2 4 4 6 4 8 4 1 7 5 8 9 5 9 3 2 5 8 2 2 7 2 8 4 1 9 3 6 0 2 2 9 1 2 7 2 1
[482] 3 4 9 1 8 0 2 2 3 4 1 3 7 4 1 4 1 5 9 6 9 0 5 7 6 8 2 0 7 3 5 8 2 8 2 4 8
[519] 5 8 9 7 1 2 4 5 5 1 8 1 4 4 6 5 8 9 2 3 0 5 1 4 0 5 1 2 9 2 4 1 6 8 0 4 9
[556] 0 0 5 9 2 3 5 9 4 4 3 9 2 3 5 6 5 2 7 2 4 2 4 7 2 5 3 7 6 1 0 7 5 4 5 1 6
[593] 9 7 1 6 3 3 1 2 2 0 5 0 6 8 3 6 7 7 3 8 1 7 9 3 9 2 8 3 7 4 1 2 3 6 5 0 1
[630] 8 6 9 2 1 6 0 2 8 0 8 8 9 1 2 2 1 4 8 1 4 4 5 1 8 7 7 9 7 0 6 9 4 5 6 2 5
[667] 7 4 7 2 3 0 8 4 8 0 0 9 7 7 9 8 2 1 6 5 5 1 1 9 7 7 8 6 4 7 5 3 1 6 4 5 7
[704] 4 1 8 3 5 1 7 1 1 8 6 4 3 8 3 1 2 8 9 0 9 1 2 3 3 0 3 0 2 0 3 3 8 3 5 7 0
[741] 5 9 0 5 9 1 5 1 1 2 6 5 5 4 5 1 6 0 2 2 8 0 7 1 0 8 5 6 3 2 9 4 3 6 0 3 4
[778] 1 5 9 3 0 5 0 6 2 7 6 6 6 9 6 7 8 2 0 6 0 8 9 5 3 6 7 4 3 9 7 2 0 4 7 2 2
[815] 8 2 7 0 4 0 5 2 8 7 7 9 1 4 0 1 1 2 3 6 2 0 6 6 1 9 4 5 2 7 7 8 9 5 8 3 8
[852] 5 6 2 0 9 7 1 8 2 6 9 8 4 9 4 1 3 8 4 0 7 7 3 7 6 6 8 8 2 7 0 4 3 7 7 0 8
[889] 4 7 4 0 6 9 8 6 0 1 6 4 5 2 7 3 6 2 2 9 2 7 4 8 7 2 9 5 3 4 8 0 4 4 6 5 6
[926] 1 2 2 8 4 5 7 8 0 6 8 9 1 7 7 2 6 3 9 9 1 0 4 2 5 4 4 9 2 6 7 2 8 3 3 2 7
[963] 0 4 7 0 7 7 8 1 7 3 7 8 0 1 0 2 9 7 6 2 2 6 9 0 6 8 8 9 6 3 5 0 2 2 5 9 6
[1000] 4


Which produces the following histogram:

From what I have heard this is expected. I had assumed that a histogram would display the count of each occurrence of each number in my set. But this does not seem to be right, because 10 numbers occur in my set and there are only 9 columns in my histogram. Can someone explain what each of those 9 columns represents?

• Since you are using Matlab, use hist(A,n) to get a histogram with n bins. Aug 29 '12 at 6:08
• Actually I'm using R Aug 29 '12 at 6:12
• Rob's advice is sound and you can use table to calculate frequencies for discrete data. Aug 29 '12 at 7:13
• What does the number in [] bracket mean and where do they show on the output? Thanks. Aug 29 '12 at 7:35

Because a histogram is for continuous data, it divides the x-axis into equal sized intervals and counts up the number of observations in each interval, with intervals open on the left and closed on the right. So the intervals are $[0,1+\epsilon)$, $[1+\epsilon,2+2\epsilon)$, etc. for some small $\epsilon$.