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Q: Why is the sample standard deviation used to derive the standard error of the mean?

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Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.

If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]

Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

The sample standard error.

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Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.

The standard error is the standard deviation divided by the square root of the sample size.

If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]

Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.

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Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

The sample standard error.

There is no such thing. The standard error can be calculated for a sample of any size greater than 1.

The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).

Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.

A small sample and a large standard deviation

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