Question

Sometimes the idea the sampling distribution of the mean can be tricky to fully grasp. If you think you understand it well, then respond to the following. Imagine that you have 100 pieces of paper on a table in front of you. Each one has a single number between 1 and 100 (inclusive) written on it; each of those number is written on exactly one piece of paper. You can consider this to be a population. Assuming you knew nothing about the Central Limit Theorem, outline how you would assemble the sampling distribution.

Answer 1

Let us take 100 samples of size 10 each (with or without replacement) from the 100 pieces of paper. We pick up 10 pieces of paper for each sample.

Let one of the samples be :

58, 15, 27, 7, 4, 100, 57, 59, 27, 30

For each sample,we calculate its mean and note it down.

The sample mean for the above sample is 38.4

We repeat the same for the other 99 samples.

The sampling distribution of the mean will be the distribution of these 100 means for the 100 samples we took.

Now, we expect this sampling distribution to be approximately normally distributed. We can plot a histogram to prove our point.

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