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The margin of error calculator is a time efficient tool that saves your hours when you need to calculate random sampling error in your data/survey.

In case you need the margin of error quickly computed, our sampling error calculator is just what you need!

Margin of error is the parameter that determines by what percent the collected data about a particular subject may differ from its ground reality.

It's a parameter for expressing the number of random sampling errors in a given sample from a population. It is commonly described as the array of confidence interval for a specific statistic.

In a nutshell, you can think about it as a scale that determines/approximates how effective a particular survey would be.

The smaller the error, the likelier it is that your data results correspond to the reality of the population instead of just the sample.

It's an imperative and handy statistical tool, and is a great help for especially for marketers, surveyors, statisticians and data scientists to find margin of error statistics.

If you need to know how to find margin of error, then simply follow the steps given below:

- Input the sample size as well as the population size: the population size is required for the fact that data metrics such as standard deviation and variance are impacted when sample size is significant relative to the population.
- Input the confidence level you are aiming for. Our margin of error calculator would use this to determine the fitting Z-score.
- Then, you need to provide the probability distribution.

For the sake of demonstration, consider that your sample size is 50 while the population size is 2000, the confidence interval you’re aiming for is 95 percent and the probability distribution stands at 53 percent.

With this data provided, our Error Margin Calculator would compute in real time and provide you the answer.

**This is how it works.**

With the data given;

Sample Size = n = 50

Population Size = N = 2000

Probability = p = 53 percent

Confidence Interval = α = 95 percent

Given the **Margin of error formula**:

__MoE = z x √(p(1-p)) / √((N - 1) * n/(N-n))__

__= 1.96 x √(0.53(1-0.53)) / √((2000 - 1) * 50/(2000-50))__

__= 1.96 x √(0.53(0.47)) / √((1999 ) * 50/(1950))__

__= 1.96 x √(0.2491) / √(99950 /(1950)__

__= 1.96 x √(0.2491) / √(51.2564 )__

__= 1.96 x 0.4991 x 7.1594 x 100__

__MoE = 13.66 %__

The above process is displayed using margin of error equation just for the sake of information to give you an idea how to calculate manually.

However, doing it manually is time consuming, not to mention the lurking potential for human error can jeopardize manual calculations.

This is why, this tool has been developed. Calculating margin of error with our tool is a no brainer due to its user friendliness.

Our site does not require you to register, subscribe or pay to use this tool. It’s a totally free service in order to facilitate people involved in statistics, data science, surveys and market research among other fields.

In case you’re wondering what is Z score and how it is related to the confidence interval, we have outlined a detailed description explaining what it is to clear any possible air of confusion.

Z-score is a quantitative statistic that determines an individual value's relationship to the arithmetic mean of a set of values, determined in relation to the standard deviation from the mean.

Z-score of 0 shows that a value is same as the mean. Consequently, Z-score of 1 tells that a particular value is precisely one standard deviation from the arithmetic mean.

This margin of error calculator is one, which can determine z scores from the corresponding confidence interval. Confidence interval can be described as the likelihood that the value of a parameter is within a definite array of values.

Different areas in the scientific field commonly make use of fluctuating confidence levels. For instance, in psychological research, it is typical to go for a confidence interval of 95% that has a corresponding Z-score of 1.96.

Alternatively, in medical field, it is common to opt for higher levels, for example, as high as 99 %.

While you’re here, you can also check out our other margin of error confidence interval Calculator to work out the confidence level for your data.