What Is Margin of Error?

Written by Coursera Staff • Updated on

Learn how margin of error quantifies uncertainty, factors influencing it, and its significance in survey sampling and data analysis.

[Featured image] A data analyst explains the margin of error on a recent poll to two colleagues sitting at an office table.

Margin of error is a statistical term that represents the range of uncertainty or variability around an estimate or measurement. It quantifies the degree of confidence we can have in the accuracy of the estimate. When conducting surveys or collecting data, it is often not feasible or practical to survey the entire population. Instead, a sample is taken, and the results are used to make inferences about the larger population. The margin of error helps to account for the potential discrepancy between the sample and the population.

For example, you may want to know if your customers would support a new product release, so you poll a sampling of your existing customer base through an email survey. Since this sampling does not include all of your customers, the margin of error would account for the percentage of customers who may or may not agree with those surveyed.

The margin of error is typically expressed as a plus or minus value, and it indicates the range within which the true value is likely to fall. For example, if a survey reports a margin of error of ±3%, it means that the results are believed to be accurate within three percentage points in either direction. This means that the true value could be three percent higher or three percent lower than the reported estimate.

For example, if your poll found that 80 percent of surveyed customers approved of a new product release with a margin of error of ±3%, your actual value could range from 77 to 83. This range of values is known as the confidence interval and represents the degree of uncertainty or certainty in your estimate.

Data with a lower margin of error is more accurate and reliable than data with a higher margin of error. All data chosen as a random sample will have some uncertainty; the margin of error just explains how much.  

What impacts the margin of error?  

Three main factors will usually impact your margin of error. They are sample size, standard deviation, and confidence level. If any of those change, the margin of error will change with them. 

  • Sample size: This refers to the number of people or other entities you are including in your survey. A larger sample of a population is a more realistic representation of that population, so it's more likely to be accurate. 

  • Standard deviation: The population's standard deviation, or variability, is a measure of how far apart data points are from one another. Larger deviations mean a larger margin of error, while smaller deviations usually make for a smaller margin of error. 

  • Confidence level: Confidence level is a percentage that shows how certain you are that your sample is representative of your entire population. Commonly used confidence levels are 90%, 95%, and 99%. As the confidence level increases, the margin of error becomes wider to capture a higher level of certainty. Conversely, if a lower confidence level is chosen, the margin of error will be narrower, indicating a lower level of certainty.

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