x is the input data series (one/two dimensional array of cells (e.g. rows or columns)).

N is the input number of bins for the histogram.

k is the bin index or order; e.g. 1=1st bin (default),2=2nd bin,..., N.

Ret_type is a switch to select the return output (0=lower limit (default), 1= upper limit of the bin, 2= center of the bin).

1. The input data series may include missing values (e.g. #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
2. The lower limit (L) of a bin is calculated as follows:
   
   $$\operatorname{L}=\operatorname{max}(X) - j \cdot h$$
   
   $$h=\left \lfloor \frac{\mathrm{max}(X)-\mathrm{min}(X)}{k} \right \rfloor$$
   
   Where:
   
   • $h$ is the width of the bins
   • $j$ is the input bin index
   • $X$ is the input data series
3. The upper limit (U) of a bin is calculated as follows:
   
   $$\operatorname{U}=\operatorname{min}(X) - j \cdot h$$
   
   Where:
   
   • $h$ is the width of the bins
   • $j$ is the input bin index
   • $X$ is the input data series

Example 1:

Files Examples

Related Links

• Wikipedia - Histogram
• Wikipedia - Freedman-Diaconis rule
• MIT - Histogram Bin-width optimization

References

• Balakrishnan, N., Exponential Distribution: Theory, Methods and Applications, CRC, P 18 1996.