Margin of Error (ME) Formula & Calculator



Random Sampling Error Calculation

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Margin of Error Calculator - step by step calculation, formula & solved example problems online to determine the amount of random sampling error in experiments or survey results, from the input values of sample size, probability & population size. In statistics & probability, the larger & lower ME provides lower & higher confidence intervals.

Margin of Error & its Formula

It's a widespread abstract of sampling error, which measures an uncertainty about an experiment or test result. Generally, margin of error (ME) is 1.96 times of Standard Error. The standard error calculation can be done by the mathematical formula SE = (√((p(1-p)/n) )). Therefore ME = 1.96 x √((p(1-p)/n) ). 1.96 is the z-score for 95% confidence (commonly used), 1.64 is the z-score for 90% confidence level and 2.58 is the z-score for 99% confidence level. Margin of error arises whenever a population is incompletely sampled. The higher value provides lower confidence interval & the lower value provides higher confidence interval.

The below mathematical formula is used in this calculator to determine the uncertainty of an experiment result based on the input values of sample size n, probability p & population size N.

formula to estimate margin of error ME = 1.96 x √((p(1-p)/n) )

Solved Example

The below solved example may be useful to understand how the values are being used in the mathematical formulas to estimate the margin of error in statistical & probability experiment or survey results. The z-score 1.96 is commonly used value in this formula and it may gets changed sometimes based on the other confidence levels 90% & 99%, so please carefully select the z-score for the expected confidence level.

Example Problem :
Estimate the margin of error (ME) for the experiment having the probability expectation p = 0.3, confidence interval 95% & the sample size n = 1000?

Solution :
Data given
probability p = 0.3
confidence level = 95%
so the z-score is 1.96 for 95% confidence interval
z = 1.96
sample size n = 1000

Step by step calculation
formula to find ME = z √(p(1-p)/n)
substitute the values in the above formula
= 1.96 x √(0.3 x 0.7/1000)
ME = 0.028

The ME formulas, step by step calculation & solved example may be useful to understand the complete calculation, but for quick calculations, when it comes to online, this margin of error (ME) calculator may be useful to perform & verify such calculations quick as possible to analyze & summarize the statistical data.



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