An example of equal width, specifically in the context of equal-width binning, is dividing a range of data values into segments of the same size.
Understanding Equal-Width Binning
Equal-width binning is a data preprocessing technique used to group numerical data into a fixed number of intervals or "bins", where each interval spans the same range of values. This method simplifies data and can make patterns easier to identify.
The key characteristic is that the width of each bin is constant across the entire range of the data.
A Clear Example
According to the provided reference, a straightforward example of equal-width binning is demonstrated with a specific dataset range and number of bins:
For example, if the values range from 0 to 100, and we want 10 bins, each bin will have a width of 10.
In this scenario:
- Data Range: The numerical values are spread between 0 and 100.
- Number of Bins: We decide to create 10 distinct groups or bins.
- Calculation: To find the width of each bin, the total range (100 - 0 = 100) is divided by the number of bins (10). 100 / 10 = 10.
- Result: Each bin will cover a range of 10 values.
Visualizing the Bins
Based on the example, the 10 bins would look like this:
| Bin Number | Value Range |
|---|---|
| 1 | 0 up to 10 |
| 2 | 10 up to 20 |
| 3 | 20 up to 30 |
| 4 | 30 up to 40 |
| 5 | 40 up to 50 |
| 6 | 50 up to 60 |
| 7 | 60 up to 70 |
| 8 | 70 up to 80 |
| 9 | 80 up to 90 |
| 10 | 90 up to 100 |
Note: The boundaries of bins need careful definition (e.g., whether the upper limit is inclusive or exclusive), but the core concept of equal width remains.
Why Use Equal Width?
As noted in the reference, this method offers several advantages:
- Ease of Implementation: It's a simple calculation to determine bin width.
- Interpretability: The bins are easy to understand because they represent consistent intervals.
- Preserves Distribution: It tends to maintain the general shape of the data's distribution, especially if the data is uniformly distributed.
This example clearly illustrates how equal width applies to dividing a continuous range into discrete, uniformly sized intervals.
