How To Calculate Margin Of Error (With Examples)

If you’ve ever considered a statistic or consulted a particular research study when making important career decisions, then understanding what margin of error is and how it applies to you is essential to your professional career and future success.

Computing percentages and having a solid grasp on the specific principles involved with a margin of error is no longer reserved simply for statisticians and mathematicians. Having the ability to determine the margin of error and recognize what that number means is an important skill to have in virtually every occupation and professional industry in the United States.

The margin of error is especially useful as it takes uncertainty percentages into account. When it comes to analyzing career statistics, conducting customer polls and surveys, reviewing staff questionnaires, and more, the margin of error can be a telling figure.

Understanding and calculating the margin of error are important for all job seekers, employees, managers, executives, and employers. Using the tips outlined in this article, you’ll be well on your way to increasing your knowledge of margin of error and understanding the methods and principles used to calculate such percentages.

What Is Margin of Error?

The margin of error is a statistical term used to refer to a range of values higher or lower than a sample statistic which is calculated to illustrate the statistical uncertainty of the results of a survey or poll. To put it simply, the margin of error is a measurement of error in a specific sample statistic.

When discussing the margin of error, it’s important to note that the calculation refers to the error, or uncertainty, in terms of sampling. The margin of error does not, however, take survey calculation errors into account.

When a sample survey or poll is conducted, and researchers did not or were unable to include everyone in the given sample population, a sampling error will emerge since the recorded results could differ from the survey outcome, which had all intended parties been included. The margin of error records this sampling error.

The margin of error is calculated using the critical value, the sample proportion, the standard deviation, or standard error, and the sample size and is represented by a numerical percentage.

In general, the higher the margin of error is, the higher chance there is that the survey, poll, or statistic is not a complete and accurate representation of the sampled population.

As such, when relying on statistics to make business or career decisions, it’s important to fully analyze the margin of error in order to be well informed on the accuracy of the results and capable of making the best possible decision based on those findings.

How to Calculate Margin of Error

Calculating the margin of error can be a bit complicated, but if you take it step by step and closely follow the calculation tips discussed below, you’ll be able to quickly and accurately calculate the margin of error for any statistical survey, questionnaire, or poll.

As discussed above, the margin of error can be calculated for any given survey or poll using the critical value, the sample proportion, the standard deviation, or standard error, and the sample size. The resulting number is a numerical percentage that represents the margin of error.

The formula to calculate margin of error takes the critical value and multiples it by the square root of the sample proportion times one minus the sample proportion divided by the sample size.

In mathematical terms, the formula to determine margin of error is represented as follows:

The critical value, represented in the formula by the letter “Z,” is, in layman’s terms, the confidence level for the given sample.

The critical value is typically displayed using a z-score of a T-score. In general, t-scores are used for smaller sample sizes under 30 or when the standard deviation is unknown. In all other scenarios, z-scores are most often used to determine the margin of error.

To determine the critical value, a z-score must be calculated.

This can be done by determining the confidence interval of the sample and using the z-score associated with that interval or by subtracting the mean of the population or sample from the variable from the population and dividing that number by the standard deviation, or standard error, for the sample, which can be determined using the population parameters.

Once the critical value is determined, calculating the margin of error becomes quite simple.

Following the formula above, you should input each number into the correct area, being sure to enter the sample proportion as a decimal. Once all numbers are properly inputted, the calculations can be completed, and the margin of error can be accurately computed.

Example of Calculating Margin of Error

To help you fully understand the complexities of calculating the margin of error, we’ve created the below sample scenario, which can be used as a guide or template when calculating your own margin of error for a specific survey sample.

Here is a simple example of how to efficiently calculate margin of error:

Final Thoughts

As odd as it may sound, understanding and calculating the margin of error is an important skill that every working professional should have — not just studying or working in mathematics or statistics.

Since virtually every industry in the United States routinely conducts polls and surveys, whether on sales, customer trends, or employee satisfaction rates, calculating the margin of error is an essential ability for employers and an important notion for job seekers and employees alike to understand.

Understanding the margin of error in important studies, surveys, and statistics can help you determine the accuracy and validity of various results and make educated and informed decisions on important career moves and business strategies.

Author

Elsie Boskamp

Elsie is an experienced writer, reporter, and content creator. As a leader in her field, Elsie is best known for her work as a Reporter for The Southampton Press, but she can also be credited with contributions to Long Island Pulse Magazine and Hamptons Online. She holds a Bachelor of Arts degree in journalism from Stony Brook University and currently resides in Franklin, Tennessee.