No menu items!

What happens to the expected value of m as sample size increases?

-

As the sample size increases, the expected value of the sample mean (denoted as m) tends towards the population mean.

Suppose that we are given a population that has a fixed mean. We keep on drawing samples of larger and larger size in order to understand the population. We denote the sample mean as ‘m’.

Since the sample mean changes as we keep on drawing different samples, we can treat the sample mean as a random variable and calculate the expected value of the sample mean.

The weak law of large numbers tells us about the behaviour of the expected value of the sample mean. It tells us that the expected value of ‘m’ tends closer and closer to the population mean as the sample size increases.

Hey 👋

I'm currently pursuing a Ph.D. in Maths. Prior to this, I completed my master's in Maths & bachelors in Statistics.

I created this website for explaining maths and statistics concepts in the simplest possible manner.

If you've found value from reading my content, feel free to support me in even the smallest way you can.



Share this article

Recent posts

Popular categories

Recent comments