statrefs home‎ > ‎Main‎ > ‎Methods‎ > ‎Graphical Methods‎ > ‎

Histogram


 
under construction







 

Related to Density Estimation and Density Plots (Wikipedia), as well as Spectral Density and also Kernel Density Estimation (Wikipedia).



NOTE - this information is listed for reference only; no recommendations are made regarding any method or approach.


Histogram:  How many observations?

There are various guidelines.  Here are a few that might be encountered:  Some say no less than 30 observations.  Another guideline is 50 to 100 observations.

And while the number of observations is important, it might be considered equally important that the observations are a random sample from the process.



Histogram:  How many bins?

The question of bin size (cell size) and the number of bins is related to filter theory and the question of Bandwidth.  Making the bins very narrow captures high frequency information that may not add much toward the goal of understanding the data and associated process, while making the cells very wide filters out (smooths) the high frequency information.  There is no strict mathematical guideline (of which I am aware) that fits every situation.

There are various schools of thought.  A few are noted below. 

NOTE - this information is listed for reference only; no recommendations are made regarding any method or approach.


  • Montgomery SQC
    • The number of bins depends on the sample size; five to twenty bins is sufficient for most applications.  (page 44)
    • Reference is made to Sturgis' rule, and a suggestion is offered that it may be sufficient to use a number of bins that is equal to the square root of the number of observations.

  • Process Quality Control (Ott)
    • Section 1.4
    • Sturges' rule of thumb for cell size - relationship between sample size (n) and number of cells (c)
      • c = 1 + 3.3*log10(n)
      • ... or n = 2(c - 1)
    •  Table from Ott (page 10):

 Sample Size
(n)
 Number of cells
(c)
 6 to 11
 4
 12 to 23
 5
 24 to 46
 6
 47 to 93
 7
 94 to 187
 8
 188 to 376
 9
 377 to 756
 10
 757 to 1,519
 11
 1,520 to 3,053
 12
 3,054 to 6,135
 13
 6,136 to 12,328
 14
 12,329 to 24,770
 15





Comments