I have a big continuous array of values that ranges from (-100, 100)
Now for this array I want to calculate the weighted average described here
since it's continuous I want also to set breaks for the values every 20 i.e the values should be discrete as -100 -80 -60 .... 60 80 100
How can I do this in NumPy or python in general?
EDIT: the difference here from the normal mean, that the mean is calculated according to the frequency of values
Best How To :
You actually have 2 different questions.
- How to make data discrete, and
- How to make a weighted average.
It's usually better to ask 1 question at a time, but anyway.
Given your specification:
xmin = -100
xmax = 100
binsize = 20
First, let's import numpy and make some data:
import numpy as np
data = numpy.array(range(xmin, xmax))
Then let's make the binnings you are looking for:
bins_arange = numpy.arange(xmin, xmax + 1, binsize)
From this we can convert the data to the discrete form:
counts, edges = numpy.histogram(data, bins=bins_arange)
Now to calculate the weighted average, we can use the binning middle (e.g. numbers between -100 and -80 will be on average -90):
bin_middles = (edges[:-1] + edges[1:]) / 2
Note that this method does not require the binnings to be evenly "spaced", contrary to the integer division method.
Then let's make some weights:
weights = numpy.array(range(len(counts)) / sum(range(len(counts))
Then to bring it all together:
average = np.sum(bin_middles * counts * 1) / sum(counts)
weighted_average = np.sum(bin_middles * counts * weights) / sum(counts)