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.

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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.

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.

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

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

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

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%

*Margin of error* | Statistics How To.

*Your guide to margin of error |* Qualtrics.

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