- Glossary
- What Is Gross Monthly Income?
- What Is Management?
- What Is A Problem Statement?
- What Is Annual Net Income?
- What Is A Letter Of Transmittal?
- What Is Attrition?
- What Does White Collar Mean?
- What Does Blue Collar Mean?
- What Is Efficiency Vs Effectiveness?
- What Is A Dislocated Worker?
- What Is Human Resource (HR)?
- Thank You Letter Scholarships
- What Is Constructive Criticism?
- What Is A Quarter Life Crisis?
- What Is Imposter Syndrome?
- What Is Notes Payable?
- Types Of Communication
- Economic Demand
- Cost Benefit Analysis
- Collective Bargaining
- Key Performance Indicators
- What Is Gender Bias In A Job Description?
- What Is The Hidden Job Market?
- What Is The Difference Between A Job Vs. A Career?
- What Is A Prorated Salary?
- W9 Vs. 1099
- Double Declining Balance Method
- Divergent Vs Convergent Thinking
- Budgeting Process
- Types Of Intelligence
- What Is Bargaining Power?
- What Is Operating Capital?
- Difference Between Margin Vs Markup
- Participative Leadership
- Autocratic Leadership
- Authoratarian Leadership
- Situational Leadership
- Difference Between Generalist Vs Specialist
- Strategic Leadership
- Competitive Strategies
- Equity Vs Equality
- What Is Marginalization?
- Colleague Vs Coworker
- What Is The Glass Ceiling?
- What Are Guilty Pleasures?
- Emotion Wheel
- Nepotism In The Workplace
- Sustainable Competitive Advantage
- Organizational Development
- Communication Styles
- Contingent Workers
- Passive Vs Non Passive Income
- Choose A Career
- Formulas
- APR Formula
- Total Variable Cost Formula
- How to Calculate Probability
- How To Find A Percentile
- How To Calculate Weighted Average
- What Is The Sample Mean?
- Hot To Calculate Growth Rate
- Hot To Calculate Inflation Rate
- How To Calculate Marginal Utility
- How To Average Percentages
- Calculate Debt To Asset Ratio
- How To Calculate Percent Yield
- Fixed Cost Formula
- How To Calculate Interest
- How To Calculate Earnings Per Share
- How To Calculate Retained Earnings
- How To Calculate Adjusted Gross Income
- How To Calculate Consumer Price Index
- How To Calculate Cost Of Goods Sold
- How To Calculate Correlation
- How To Calculate Confidence Interval
- How To Calculate Consumer Surplus
- How To Calculate Debt To Income Ratio
- How To Calculate Depreciation
- How To Calculate Elasticity Of Demand
- How To Calculate Equity
- How To Calculate Full Time Equivalent
- How To Calculate Gross Profit Percentage
- How To Calculate Margin Of Error
- How To Calculate Opportunity Cost
- How To Calculate Operating Cash Flow
- How To Calculate Operating Income
- How To Calculate Odds
- How To Calculate Percent Change
- How To Calculate Z Score
- Cost Of Capital Formula
- How To Calculate Time And A Half
- Types Of Variables
Find a Job You Really Want In
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:
Margin of error = Z * √ ( (p*(1 – p)) / n)
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:
A company was conducting a customer survey to determine how many of their clients use the exercise equipment they purchased from their online fitness retail shop. They surveyed 1000 of their most recent customers and found that 720 of them used the workout equipment regularly or at least twice a week.
The confidence interval for the survey was 95%, which correlates with a z-score, or critical value, of 1.96. Using this information and the survey results and size, we can easily determine the margin of error for this particular sample.
To calculate this margin of error, we would need to take the critical value of 1.96 and multiply it by the square root of the sample proportion, which equals 0.72, times one minus the sample proportion of 0.72 divided by the sample size of 1000.
In mathematical terms, the formula to determine this particular margin of error is represented as follows:
Margin of error = 1.96 * √ ( (0.72*(1 – 0.72)) / 1000)
After solving this equation, the resulting number is 0.02783, which can be converted into a percent by multiplying the decimal by 100. This leaves us with a margin of error of 2.783%.
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.
- Glossary
- What Is Gross Monthly Income?
- What Is Management?
- What Is A Problem Statement?
- What Is Annual Net Income?
- What Is A Letter Of Transmittal?
- What Is Attrition?
- What Does White Collar Mean?
- What Does Blue Collar Mean?
- What Is Efficiency Vs Effectiveness?
- What Is A Dislocated Worker?
- What Is Human Resource (HR)?
- Thank You Letter Scholarships
- What Is Constructive Criticism?
- What Is A Quarter Life Crisis?
- What Is Imposter Syndrome?
- What Is Notes Payable?
- Types Of Communication
- Economic Demand
- Cost Benefit Analysis
- Collective Bargaining
- Key Performance Indicators
- What Is Gender Bias In A Job Description?
- What Is The Hidden Job Market?
- What Is The Difference Between A Job Vs. A Career?
- What Is A Prorated Salary?
- W9 Vs. 1099
- Double Declining Balance Method
- Divergent Vs Convergent Thinking
- Budgeting Process
- Types Of Intelligence
- What Is Bargaining Power?
- What Is Operating Capital?
- Difference Between Margin Vs Markup
- Participative Leadership
- Autocratic Leadership
- Authoratarian Leadership
- Situational Leadership
- Difference Between Generalist Vs Specialist
- Strategic Leadership
- Competitive Strategies
- Equity Vs Equality
- What Is Marginalization?
- Colleague Vs Coworker
- What Is The Glass Ceiling?
- What Are Guilty Pleasures?
- Emotion Wheel
- Nepotism In The Workplace
- Sustainable Competitive Advantage
- Organizational Development
- Communication Styles
- Contingent Workers
- Passive Vs Non Passive Income
- Choose A Career
- Formulas
- APR Formula
- Total Variable Cost Formula
- How to Calculate Probability
- How To Find A Percentile
- How To Calculate Weighted Average
- What Is The Sample Mean?
- Hot To Calculate Growth Rate
- Hot To Calculate Inflation Rate
- How To Calculate Marginal Utility
- How To Average Percentages
- Calculate Debt To Asset Ratio
- How To Calculate Percent Yield
- Fixed Cost Formula
- How To Calculate Interest
- How To Calculate Earnings Per Share
- How To Calculate Retained Earnings
- How To Calculate Adjusted Gross Income
- How To Calculate Consumer Price Index
- How To Calculate Cost Of Goods Sold
- How To Calculate Correlation
- How To Calculate Confidence Interval
- How To Calculate Consumer Surplus
- How To Calculate Debt To Income Ratio
- How To Calculate Depreciation
- How To Calculate Elasticity Of Demand
- How To Calculate Equity
- How To Calculate Full Time Equivalent
- How To Calculate Gross Profit Percentage
- How To Calculate Margin Of Error
- How To Calculate Opportunity Cost
- How To Calculate Operating Cash Flow
- How To Calculate Operating Income
- How To Calculate Odds
- How To Calculate Percent Change
- How To Calculate Z Score
- Cost Of Capital Formula
- How To Calculate Time And A Half
- Types Of Variables