Expected Value In Statistics Definition Examples

Expected Value in Statistics Definition

The formula for expected valueFormula For Expected ValueThe expected value formula depicts the possible value of an investment or asset in a future period. It is evaluated as the sum of the occurrence probabilities of all the random variables.read more is simple:

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Px = Probability distributionX = 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 we are not given the probability of the numbers, 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 it is given the probability 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 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 weeks when you went on all seven days. It helps to 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 mathematical skills to calculate the expected value.Consider every possibility of outcome to calculate the expected value.

Disadvantages

It is based on mathematical calculations and is a numerical representation of the future valueFuture ValueThe Future Value (FV) formula is a financial terminology used to calculate cash flow value at a futuristic date compared to the original receipt. The objective of the FV equation is to determine the future value of a prospective investment and whether the returns yield sufficient returns to factor in the time value of money.read more of any investment.The EV depends on probability, which is highly subjective.It is an average of all possible outcomes. Hence, it does not give the actual result or outcome.One cannot use it for a one-time activity but scenarios with repeated outcomes.It does not give a view of the risk involved.It may not 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).It is not recommended for a one-time or infrequent scenario since EV derives from various trials.It provides a fair idea of the future value of an investment.EV is not foolproof, yet the result obtained from the calculation can prove useful during decision-making.

Conclusion

It is the future value of an investment or a product based on various possibilities, like the change in the value from time to time and the period for which the price is considered.It is calculated mathematically by multiplying the outcomes with a probability distributionProbability DistributionProbability distribution could be defined as the table or equations showing respective probabilities of different possible outcomes of a defined event or scenario. In simple words, its calculation shows the possible outcome of an event with the relative possibility of occurrence or non-occurrence as required.read more and adding them.The EV can differ from the calculated expected value since it is based on assumptions. Still, it can provide a pathway to understanding roughly where the expected value will be.Investors can rely on expected value to decide whether investing is worthy and can reap the maximum out of their investment.