Python Implementation of The Central Limit Theorem
We will generate random numbers from -40 to 40 and and collect their mean in a list. we will itratively perform his operation for different count of numbers and we will plot their sampling distribution.
python3
import numpyimport matplotlib.pyplot as plt# number of samplenum = [1, 10, 50, 100] # list of sample meansmeans = [] # Generating 1, 10, 30, 100 random numbers from -40 to 40# taking their mean and appending it to list means.for j in num: # Generating seed so that we can get same result # every time the loop is run... numpy.random.seed(1) x = [numpy.mean( numpy.random.randint( -40, 40, j)) for _i in range(1000)] means.append(x)k = 0# plotting all the means in one figurefig, ax = plt.subplots(2, 2, figsize =(8, 8))for i in range(0, 2): for j in range(0, 2): # Histogram for each x stored in means ax[i, j].hist(means[k], 10, density = True) ax[i, j].set_title(label = num[k]) k = k + 1 plt.show() |
Output:
Central limit theoram for getting normal distribution
It is evident from the graphs that as we keep on increasing the sample size from 1 to 100 the histogram tends to take the shape of a normal distribution.
Python â Central Limit Theorem
Statistics is an important part of Data science projects. We use statical tools whenever we want to make any inference about the population of the dataset from a sample of the dataset, gather information from the dataset, or make any assumption about the parameter of the dataset. In this article, we will talk about one of the important statical tools central limit theorem.
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