Standard Error Calculator
Calculate the standard error of the mean, which measures how much the sample mean varies from sample to sample.
Erreur type
3.000000
Standard Error vs Standard Deviation
Formule
## How to Calculate the Standard Error ### Formula **SE = sigma / sqrt(n)** The standard error of the mean measures the precision of the sample mean as an estimator of the population mean. It is the standard deviation of the sampling distribution of the mean. As sample size increases, SE decreases, making estimates more precise.
Exemple Résolu
Population SD = 15, sample size = 25. What is the standard error?
- 01SE = sigma / sqrt(n)
- 02SE = 15 / sqrt(25)
- 03SE = 15 / 5 = 3
- 04Variance of mean = 15^2 / 25 = 225 / 25 = 9
Questions Fréquentes
What is the difference between standard deviation and standard error?
Standard deviation measures the spread of individual observations. Standard error measures the spread of sample means. SE is always smaller than SD (by a factor of sqrt(n)) because averaging reduces variability.
Why does SE decrease with larger samples?
Larger samples average out individual variability more effectively. The mean of 100 observations is more stable than the mean of 4 observations, hence the sqrt(n) in the denominator.
Can I use sample SD instead of population SD?
Yes. In practice, the population SD is rarely known, so we use the sample SD (s) as an estimate. The result is an estimated standard error, and we typically use the t-distribution instead of z for inference.
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