## Expected Value in Statistics Definition

ExpectedValue (EV) is a mathematical calculation that finds the anticipated value of an investment on the basis of various possibilities that are taken into consideration (like the change in the value from time to time and the time period for which the price is being considered). It can be calculated using the outcomes and the likelihood of these outcomes to occur. It helps an investor to zero-in on most beneficial investment.

The formula for expected value is simple:

**Expected Value = ∑ Px * X**

**Px****=**Probability distribution**X****=**Outcomes

### Examples of EV

Below are some examples of the expected value.

#### Example #1

- The best example to understand the expected value is the dice. A dice has 6 sides, and the probability of getting a number between 1 to 6 is 1/6.
- If we assume X as the outcome of a rolled dice, X is the number that appears on the top of the rolled dice.
- Since the probability of the numbers is not given, we will go ahead with the probability of 1/6 in our calculations.

The calculation for EV will be as below:

#### Example #2

The below-given table shows the number of days you’ll go to the gym and its probability.

- If you see, add up the probability in the table above.

- Since the probability is given in this case, we can directly calculate the expected value by multiplying the number of days with the probability.

According to the above information, the expected number of days to head to the gym is roughly two days a week. As per the calculation, it is 1.95, so this means you can say that in 20 weeks, you went to the gym 39 times (1.95 * 20).

There might be weeks when you didn’t visit the gym, and there might be weeks when you went on all seven days. It helps understand that even though the distribution of days attending the gym might not be constant, it is still possible to get a rough estimate.

### Advantages

- Helps investors and managers in deciding on projects based on expected ROI.
- Highlights red flags in case an investment is going to underperform.
- Various outcomes are combined to arrive at a single outcome, which eases decision making.
- The easy calculation makes it accessible for anyone with basic mathematic skills to calculate the expected value.
- Considers every possibility of outcome to calculate the expected value.

### Disadvantages

- It is based on mathematical calculations and is a numerical representation of the future value of any investment.
- The EV depends on probability, which is highly subjective.
- It is an average of all possible outcomes, and hence it does not give the actual result or outcome.
- It cannot be used for a one-time activity but for scenarios where the outcome is repeated.
- It does not give a view of the risk involved.
- It may not actually correspond to any of the possible outcomes.

### Important Points

- In probability, the expected value is the weighted average of all possible outcomes with the weights given by the theoretical probabilities. It is represented by E(x).
- Since EV is derived by considering various trials, it is not recommended for a one time or infrequent scenario.
- It provides a fair idea of how the future value of an investment.
- EV is not foolproof, yet the result obtained from the calculation can prove useful at the time of decision making.

### Conclusion

- It is the future value of an investment or a product based on various possibilities that are taken into consideration, like the change in the value from time to time and the time period for which the price is being considered.
- It is calculated mathematically by multiplying the outcomes with a probability distribution and adding all of them.
- In reality, the EV can differ from the calculated expected value since it is based on assumptions. Still, it can provide a pathway to understand roughly where the expected value will be.
- Investors can rely on expected value to decide on whether investing is worthy and can reap the maximum out of their investment.

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