# Question: Are mean and expectation value the same?

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Mean or Average and Expected Value only differ by their applications, however they both are same conceptually. Expected Value is used in case of Random Variables (or in other words Probability Distributions). Since, the average is defined as the sum of all the elements divided by the sum of their frequencies.

## Is mean also expected value?

Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches infinity. The EV is also known as expectation, the mean or the first moment.

## What is the relationship between the mean of a distribution and the expected value for the distribution?

1. The mean of the distribution of sample means is called the Expected Value of M and is always equal to the population mean μ.

## What is the relationship between the expected value of the sample mean and the population mean?

The expected value of the sample mean is the population mean, and the SE of the sample mean is the SD of the population, divided by the square-root of the sample size.

## Why is it important to know the expected value or mean of a probability distribution?

An expected value gives a quick insight into the behavior of a random variable without knowing if it is discrete or continuous. Therefore, two random variables with the same expected value can have different probability distributions.

## Is the sample mean equal to the population mean?

Statisticians have shown that the mean of the sampling distribution of x̄ is equal to the population mean, μ, and that the standard deviation is given by σ/ √n, where σ is the population standard deviation. The standard deviation of a sampling distribution is called the standard error.

## What is the importance of an expected value?

An expected value gives a quick insight into the behavior of a random variable without knowing if it is discrete or continuous. Therefore, two random variables with the same expected value can have different probability distributions.