find out how 'peaky' histogram is

I have a histogram made of number of detections made by an application: 9 instances of detecting 1, 1 instances of detecting 2 and so on.

Say I have these histograms:

first histogram: 9 1 1

second histogram: 9 2 0

I'd like to know the 'confidence' of the histogram so I can find out which one is better. The first or the second. In other words, if the histogram has one big peak and the rest of values are very low, then this histogram is the best one I have.

another example:

70% 30%

70% 15% 15%

And so on..

I am probably missing the scientific term here, so any direction or help would be great. Thanks.

• People usually talk about shape and spread of a distribution. The mean, spread, and shape should completely determine a distribution (although describing the "shape" is not always easy). See this. Oct 10 '14 at 9:58

Good morning! A generally accepted consensus among statisticians is that a histogram should be divided into $\sqrt{n}$ intervals, where $n$ is the number of observations. In Your case, you have 11 observations, hence $\sqrt{11}\doteq 3.32$, which is 3 after rounding to the nearest integer. In conclusion, I recommend you the second histogram.