Procedure

Illustration of Central Limit Theorem

This experiment aims to provide an intuitive idea of how central limit theorem is useful using visualization of CLT for various distributions like uniform, gaussian, exponential, poisson, etc..

• Choose a distribution from the list of uniform, exponential, normal, or poisson
• Use the slider to choose a sample size. This determines how accurate the mean of a sample is.
• Use the 2nd slider to choose the number of samples. This decides how many sample means we want to plot. Larger this value, more accurate the sample means distribution is to the Normal fit.
• Refer to observations panel for comments about these parameters.
• Notice that no-matter the distribution, the distribution of sample means converges to a Normal Distribution if the number of samples are sufficient.

Application of CLT in Election polls

This experiment illustrates how exit polls are done during election. It demonstrates how factors like size of population sampled and desired confidence level decide the margin of error in exit polls.

• Select the number of candidates and voters using the provided dropdowns.
• Click on the candidates to cast votes.
• The chart will dynamically update, showing the vote distribution.
• Now fill the confidence required, and its corresponding critical value. Check the value to proceed furthur.
• Find the standard error using standard deviation of the sampled population and compute margin of error using it.