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Standard Error Calculator

Use this SEM calculator to calculate the standard error of the mean from raw or summary data.

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This standard error calculator calculates how much your sample mean fluctuates with respect to the population mean. Get accurate results with step-by-step solutions for sample or raw data to improve your confidence level in the given data.

What is Standard Error?

The standard error (SE) measures the accuracy of a sample mean by using its standard deviation. It indicates how much variability to expect when taking multiple samples from the same population. SE is also called the standard error of the mean (SEM).

How to Use this Standard Error Calculator?

To use this online SE calculator, follow the steps below:

Select the data type: Choose ‘Raw Data’ if you have individual data values, or ‘Summary Data’ if you already know the standard deviation and sample size.
Enter the required values: Enter the values according to your selection
Click CALCULATE: Click to process the entered values and get the final solution.
Review the results: Check the standard error (SE), the relevant statistical values, and the step-by-step calculation.

Standard Error Formula:

The standard error equation depends on whether the population standard deviation is known or estimated from a sample:

Standard Error with Raw Data:

When the population standard deviation is known:

SE= 𝜎/√n

Key Variables:

σ = Population standard deviation
n = Sample size

Standard Error with Sample Data:

When the population SD is unknown and is estimated from the sample:

SE = s/√n

Key Variables

s = Sample standard deviation
n = Sample size

How to Calculate Standard Error (Step-by-Step)?

This SEM calculator finds the standard error (SE) for raw or summary data using the standard deviation and sample size. To calculate the Standard Error of the Mean (SEM), follow these steps:

1. Identify the data: Determine whether you have raw or sample data.

Suppose you have the following raw data: 10, 12, 14, 16, 18

2. Find the standard deviation: Calculate ‘σ’ for raw data or ‘s’ for sample data.

The given values represent raw data, so we use the population standard deviation (σ). So, the population standard deviation is: σ = 2.83

3. Find the sample size (n): Count the total number of observations.

There are 5 observations, so: n = 5

4. Choose the formula: Use σ/√n for population standard deviation or s/√n for sample standard deviation.

Since we are using the population standard deviation, use:

SEM = σ/√n

5. Calculate the standard error: Divide the appropriate standard deviation by √n to get the standard error

Substitute the values:

SEM = 2.83/√5

SEM = 2.83/2.236

SEM ≈ 1.27

Therefore, the Standard Error of the Mean (SEM) is approximately 1.27.

If you have a standard error problem to solve, just enter your known values into this standard error of the mean calculator, and let it calculate the answer for you.