Freedman–Diaconis rule
The freedman-diaconis rule is a way to choose how wide to make the bins (or buckets) when you are creating a histogram. A histogram is a way of showing how many times different numbers or measurements appear in a set of data.
To use the freedman-diaconis rule, you take the range of your data (which means the biggest number minus the smallest number) and divide it by a number that is based on how many data points you have.
The bigger your range or the more data points you have, the wider your bins need to be so that the histogram is not too crowded, but not too spread out either. The freedman-diaconis rule helps you find a good balance.
So, let's say you have a set of data with 100 measurements that range from 0 to 200. First, you would find the range: 200 - 0 = 200.
Now, you need to figure out how many bins to use. The freedman-diaconis rule says you should divide the range by 2 times the square root of the number of data points:
bin width = range / (2 * √(number of data points))
For our example:
bin width = 200 / (2 * √(100))
bin width = 200 / 20
bin width = 10
This means that each bin should be 10 units wide, and you can make a histogram that shows how many measurements fall into each bin.
So, if you have measurements of 2, 5, 7, 12, 20, 28, 34, 45, 63, 89, 123, 145, 166, and 190, you can create the following histogram:
0-10: 2, 5, 7
10-20: 12, 20
20-30: 28
30-40: 34
40-50: 45
50-60:
60-70: 63
70-80:
80-90: 89
90-100:
100-110: 123
110-120:
120-130:
130-140:
140-150: 145
150-160:
160-170: 166
170-180:
180-190: 190
190-200:
This helps you visualize the distribution of your data and see where most of the measurements fall.
To use the freedman-diaconis rule, you take the range of your data (which means the biggest number minus the smallest number) and divide it by a number that is based on how many data points you have.
The bigger your range or the more data points you have, the wider your bins need to be so that the histogram is not too crowded, but not too spread out either. The freedman-diaconis rule helps you find a good balance.
So, let's say you have a set of data with 100 measurements that range from 0 to 200. First, you would find the range: 200 - 0 = 200.
Now, you need to figure out how many bins to use. The freedman-diaconis rule says you should divide the range by 2 times the square root of the number of data points:
bin width = range / (2 * √(number of data points))
For our example:
bin width = 200 / (2 * √(100))
bin width = 200 / 20
bin width = 10
This means that each bin should be 10 units wide, and you can make a histogram that shows how many measurements fall into each bin.
So, if you have measurements of 2, 5, 7, 12, 20, 28, 34, 45, 63, 89, 123, 145, 166, and 190, you can create the following histogram:
0-10: 2, 5, 7
10-20: 12, 20
20-30: 28
30-40: 34
40-50: 45
50-60:
60-70: 63
70-80:
80-90: 89
90-100:
100-110: 123
110-120:
120-130:
130-140:
140-150: 145
150-160:
160-170: 166
170-180:
180-190: 190
190-200:
This helps you visualize the distribution of your data and see where most of the measurements fall.