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.

  • $\begingroup$ 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. $\endgroup$ 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.

  • $\begingroup$ The histogram is computer made, which means that the number of intervals change depending on the application itself only. I am trying to find a formula which returns a value that tells me how 'good' and 'confident' the histogram is. (peaky) $\endgroup$
    – nonick
    Oct 10 '14 at 10:07
  • $\begingroup$ This is up to you. You are the only person that can say whether the histogram helped you to visualize your problem and whether the histogram is appropriate in other ways depending on what you have expected from it. You can thus define your own function which evaluates the quality of a histogram. $\endgroup$
    – Joseph
    Oct 10 '14 at 17:27

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