Enter your dataset values (comma-separated) or provide a standard deviation and sample size directly to calculate the Standard Error of the Mean (SE). Choose between Raw Data mode or Summary Data mode — you'll get the SE, mean, sample size (n), sum of squares, and standard deviation all at once.
Standard Error (SE)
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Number of Samples (n)
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Mean (x̄)
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Sum of Squares (SS)
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Standard Deviation (s)
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Standard Error (SE) is a statistical measure that quantifies how much variability exists between a sample mean and the true population mean. A smaller SE indicates that the sample mean is a more reliable estimate of the population mean. It is calculated by dividing the standard deviation by the square root of the sample size.
The Standard Error formula is SE = s / √n, where s is the sample standard deviation and n is the number of observations in the sample. For raw data, the standard deviation is first computed using σ = √(Σ(x − x̄)² / (n − 1)), and then divided by √n.
Select 'Raw Data' if you have individual data values — enter them comma-separated in the text area. Select 'Summary Data' if you already know the standard deviation and sample size — enter those two values directly. Click Calculate to see the SE, mean, sum of squares, and standard deviation.
Standard deviation measures the spread of individual data points around the mean within a single sample. Standard error, on the other hand, measures how much the sample mean is expected to vary from the true population mean. SE decreases as sample size increases, while standard deviation does not depend on sample size in the same way.
A low SE means your sample mean is likely very close to the true population mean, indicating high precision. This typically happens when you have a large sample size or when data points are tightly clustered. A high SE suggests more variability and less confidence in the sample estimate.
You need at least 2 data points to calculate Standard Error, since computing sample standard deviation requires dividing by (n − 1). With only 1 data point, the standard deviation is undefined and SE cannot be determined.
Yes. The SE is fundamental to building confidence intervals around the sample mean. For example, a 95% confidence interval is approximately x̄ ± 1.96 × SE, assuming a normal distribution. The SE tells you the range within which the true population mean is likely to fall.
Yes. Since SE = s / √n, doubling the sample size reduces the SE by a factor of √2 (approximately 1.41). Larger samples provide more information about the population, resulting in a more precise estimate of the mean and a smaller standard error.