Graded Questions: Central Limit Theorem

Question 1

An exit poll was conducted by a news agency for the MCD (Municipal Corporation of Delhi) elections. You had been tasked with predicting the winner for ward 75N (Ashok Vihar). For that purpose, you asked 100 randomly selected voters from your ward to name the party they had voted for.

The data thus collected is given in the following table:

  Contesting Party  
 Mean (Percentage of Voters) Standard Deviation (Percentage of Voters)
BJP 58% 49.6%
INC 42% 49.6%

Now, instead of taking more samples and forming a sampling distribution, which would be a tedious and expensive task, let’s say you decide to use your knowledge of the CLT to determine the winner.

First, you would have to form a 95% confidence interval for the percentage of voters that voted for BJP. Then, you would form another such confidence interval for INC, after which you would be able to compare the two to determine the winner.

In this way, news agencies poll people and use the data to decide the possible winner/winners for each ward. Then, they aggregate the results for all the wards and show them to us as their poll results.

The MCD elections are usually a multiparty affair, but the maths involved in the multiparty scenario would have been very difficult to understand in the present scenario. Hence, we have only taken ward 75N in this example, which was contested for by only two political parties.

If you want to read more on how exit poll maths works and how the polls are set up to ensure accuracy, you can go through the following links:

Question 2

A home renting start-up, Ghar ki Baat, is planning to offer fully furnished 2 BHK flats for rent in Powai, Mumbai. In order to ensure that it charges the correct rent, it wants to find the average rent charged by homeowners in Powai.

For that purpose, it has acquired the following data, which has a list of 200 fully furnished 2 BHK flats in Powai, along with the monthly rent charged in the year 2016.

As a data analyst working for Ghar ki Baat, you are tasked with finding the average rent for all fully furnished 2 BHK flats in Powai, Mumbai, using this data.

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