What is Central Limit Theorem | Inferential Statistics | Probability And Statist

2. What’s in it for you? What is Central Limit Theorem? Mean and Standard Deviation Real World Example Assumptions Behind CLT

3. What is Central Limit Theorem?

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5. What is Central Limit Theorem? The Central Limit Theorem (CLT) is a statistical theory that states that - if you take a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from that population will be roughly equal to the population mean Sample Population

6. Mean and Standard Deviation

7. Mean and Standard Deviation Let x̄ be a random variable representing the sample mean of n independently drawn observations

8. Real World Example Consider you're a regional manager for a pharmaceutical company, in charge of 200 stores across the region, and you're in charge of weekly medicine restocking at all the stores

9. Real World Example Mean 40 35 30 25 Count The plot on the right shows the distribution of data for all the 200 stores and the average medicine cases required by the stores in a week 20 15 10 5 0 24 42 44 26 46 48 38 32 34 18 36 20 40 22 12 10 30 16 28 14 Average Medicine Cases Required By Stores

10. Real World Example Mean 0.5 The plot on the right shows the distribution of sample means of sufficiently large subsets with size > 30 taken from the population 0.4 Frequency 0.3 0.2 0 The mean of all samples from that population is equal to the population mean = 34, and resembles of normal distribution 30 38 36 32 34 Sample Mean Distribution Of Sample Means

11. Assumptions Behind Central Limit Theorem

12. Assumptions Behind CLT The samples should be unrelated to one another. One sample should not impact the others When taking samples without replacement, the sample size should not exceed 10% of the population The data must adhere to the randomization rule. It needs to be sampled at random

13. Application Of Central Limit Theorem

14. Application Of Central Limit Theorem Political/ election polling is a great example of how you can use CLT. These polls are used to estimate the number of people who support a specific candidate. You may have seen these results with confidence intervals on news channels. The central limit theorem aids in this calculation You use the central limit theorem in various census fields to calculate various population details, such as family income, electricity consumption, individual salaries, and so on Large Population : Census data collection

15. Demo

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