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# Margin of Error Calculator

## How does Margin of Error calculator work?

The working principle of the margin of error calculator is very easy;
• Enter the sample size
• Enter the population size
• Enter the sample proportion (max = 1)
• Select the confidence level
• Hit the "calculate" button to get the step-by-step solution.
• You can erase all the values by clicking on the "reset" button.

## Margin of error calculator

The margin of error calculates the MOE using sample size (n), population size (P), sample proportion (p), and confidence level. It gives a step-by-step solution to the problem.

## What is the margin of error?

The margin of error (MOE) for a survey tells you ways close you'll be able to expect the survey results to be to the proper population price. E.g., In a random survey, we came to know that 55% of the population favored Brand X over Brand Y with 2% MOE.

According to this survey, the actual population percentage that voted for Brand X falls within the range of 55% ± 2%. MOE refers to the degree of error in the results that we get from surveys of random sampling.

## The formula for the margin of error:

There are two different cases to calculate the margin of error of a raw sample.

### Margin of error with FPC:

The formula to calculate the MOE with FPC is as follows:

MOE with finite population correction :

Now let’s have a look at the FPC, in the sample survey statistics, this concept plays a vital role. It is a factor that is used to balance the estimated variance for a hypothetical total or mean.

In the above formula,

• “P hat” is the sample proportion
• “P” is the population size
• “z” is the z-score
• “n” is the sample size

### Simple margin of error:

The simple MOE can be calculated using the following formula:

• “P hat” is the sample proportion
• “z” is the z-score
• “n” is the sample size

## Procedure to calculate the margin of error:

In this section, with the assistance of examples, the procedure is explained briefly.

Example 1:

Calculate the MOE with FPC if the sample proportion is 0.2, the population size is 1029, the sample size is 112, and the confidence interval is 95%.

Solution:

Step 1: Extract the data

Sample proportion =  = 0.2

Population size = p = 1029

The confidence interval of z at 95% = 1.960

Sample size = n = 112

Step 2: enter the values in the following formula

MOE with FPC =

MOE with FPC = 1.960 {{0.2 (1 - 0.2)}/ {112(1029 – 1)/ (1029 – 112)}

MOE with FPC = 1.960 {0.2 (0.8) / {(112) * (1028) / (917)}}}

MOE with FPC = 1.960 { 0.2(0.8)/ {112(1.121)}

MOE with FPC = 1.960 {0.16/ {125.55}}

MOE with FPC = 1.960 * 0.03569761

MOE with FPC = 0.06996

MOE with FPC = 6.997%

## References:

Margin of error | Statistics How To.

Your guide to margin of error | Qualtrics