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Standard Error Calculator FullScreen

Calculate the standard error of a sample mean or sample proportion using our online calculator. By inputting the sample standard deviation (or estimated population standard deviation), sample size, and either the population size (for proportion estimation) or leaving it blank (for mean estimation), you can determine the standard error.

Standard Error (SE) Calculator


What is Standard Error Calculator

A standard error calculator is a statistical tool used to estimate the standard deviation of a sampling distribution. It quantifies the variability or precision of sample statistics and provides important information for making inferences about the population parameters.

Here's how a standard error calculator typically works:

  1. Collect Sample Data: Gather data by taking a random sample from the population of interest. The sample size should be determined based on factors such as the desired level of precision and the variability in the population.

  2. Calculate the Sample Statistic: Depending on the type of data being collected, calculate the sample mean, proportion, or any other relevant statistic.

  3. Calculate the Standard Deviation: Calculate the standard deviation of the sample data. This measures the spread or variability within the sample.

  4. Determine Standard Error: The standard error is an estimate of the standard deviation of the sampling distribution, which describes the variability of sample statistics that could be obtained from repeated sampling. It is calculated using the formula specific to the statistic being used and the sampling method employed.

For example, if you are calculating the standard error of the mean (SEM) for a sample mean, divide the sample standard deviation by the square root of the sample size.

  1. Interpret Results: The standard error provides an indication of the uncertainty associated with the sample statistic. A smaller standard error suggests that the sample statistic is likely to be closer to the population parameter. On the other hand, a larger standard error indicates greater variability in the sample estimates.

Standard error calculators can be found online or as part of statistical software packages. They simplify the process of calculating the standard error and provide a measure of the precision of sample statistics.

If you provide me with the specific sample data, I can assist you further by calculating the appropriate standard error for your analysis.

Standard Error Formula

The Standard Error Calculator uses the following formula:

SE  x = s / sqrt( n )


SE  x   is the standard error of the mean,

s  is the standard deviation of the sample,

sqrt  is the square root,

n  is the sample size.

Example:  Assume the population standard deviation is 36. Calculate the standard error of the mean for a sample size of 49.

Solution: s = 36, n = 49

SE  x = s / sqrt( n )

SE  x = 36 / √49

SE  x = 36 / 7 = 5.1428

Therefore, the standard error of the mean for a sample size of 49 is 5.1428

Standard Error Calculator Example

Certainly! To calculate the standard error for a sample mean, you can use the formula:

Standard Error = (Standard Deviation / sqrt(n))

Here's an example to demonstrate how to calculate the standard error:

Let's say we have a dataset of exam scores from a class of 50 students. We want to estimate the average exam score for the entire population based on this sample.

Step 1: Calculate the sample mean.

Calculate the mean of the exam scores for the 50 students in our sample.

Let's assume the sample mean is 75.

Step 2: Calculate the sample standard deviation.

Calculate the standard deviation of the exam scores for the 50 students in our sample.

Let's assume the sample standard deviation is 10.

Step 3: Determine the sample size.

In this example, the sample size is given as 50.

Step 4: Calculate the standard error.

Using the formula mentioned earlier, we can calculate the standard error:

Standard Error = (10 / sqrt(50))

Calculating the square root of 50 gives us approximately 7.07.

Therefore, the standard error is:

Standard Error = 10 / 7.07 ≈ 1.415

Step 5: Interpret the standard error.

The standard error measures the average amount that the sample mean differs from the true population mean. In this example, the standard error is approximately 1.415. This means that, on average, the sample mean will differ from the true population mean by around 1.415 units.

Please note that this is just an example of calculating the standard error for a sample mean. The specific formula and calculations may vary depending on the type of estimate you are trying to calculate (e.g., proportion, difference in means, etc.) and any assumptions made in the analysis.

You may also be interested in our Percent Error Calculator