Random Sampling Error Calculator, Formula, Example Calculation
 
 

Margin of Error (ME) 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(1p)/n) )). Therefore ME = 1.96 x √((p(1p)/n) ). 1.96 is the zscore for 95% confidence (commonly used), 1.64 is the zscore for 90% confidence level and 2.58 is the zscore 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.
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 zscore 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 zscore 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 zscore is 1.96 for 95% confidence interval
z = 1.96
sample size n = 1000
Step by step calculation
formula to find ME = z √(p(1p)/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.
Similar Resource 
Trapezium Area Calculation 
Polygon Angles Calculation Worksheet 
How to Calculate Standard Error 
Worksheet for Standard Deviation Calculation 