According to a Khan Academy's lecture, the Central Limit Theorem is defined as follows:
Central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.
To test this definition I considered a population of 100,000 random numbers with the following parameters (see the image below)
Then, plotting the sampling distribution of the sample mean with varying sample sizes and sample counts resulted in the following observations (each graph is accordingly labeled).
Question: It seems to me that simply increasing the sample size is not sufficient for the distribution to become normal (based on visual observation). The number of samples also should be more.
- Then how do I reconcile these observations with the formal definition of the theorem?
- And are these conclusions correct (given the plots)?
- Increasing the sample size simply reduces the standard error
- As long as the sample size is above a minimum value, increasing the sample count seems sufficient for normality