In the formula for the standard error of the mean, s/√N, what does s represent?

In the formula for the standard error of the mean, s/√N, what does s represent?

• A. Population standard deviation
• B. Standard deviation of the sampling distribution
• C. Variance of the sampling distribution
• D. Standard deviation of the sample

Answer: (D)

The main idea here is that s is an estimate of how spread out individual observations are, and that estimate is used to gauge how far sample means would vary across repeated samples. When we don’t know the population standard deviation, we substitute the standard deviation from the sample, s, into the standard error formula. That gives s divided by the square root of the sample size, which reflects that larger samples reduce the variability of the sample mean. For intuition, if the sample standard deviation is 5 and you have a sample size of 100, the standard error is about 0.5. This means the typical fluctuation of the sample mean from one sample to another of size 100 is around 0.5. Why the other options don’t fit: the population standard deviation would be used if you knew the true population spread (not usually the case). The standard deviation of the sampling distribution is the standard error itself, not s. The variance of the sampling distribution would be the square of the standard error, not s. The standard deviation of the sample is exactly what s represents.

The main idea here is that s is an estimate of how spread out individual observations are, and that estimate is used to gauge how far sample means would vary across repeated samples. When we don’t know the population standard deviation, we substitute the standard deviation from the sample, s, into the standard error formula. That gives s divided by the square root of the sample size, which reflects that larger samples reduce the variability of the sample mean.

For intuition, if the sample standard deviation is 5 and you have a sample size of 100, the standard error is about 0.5. This means the typical fluctuation of the sample mean from one sample to another of size 100 is around 0.5.

Why the other options don’t fit: the population standard deviation would be used if you knew the true population spread (not usually the case). The standard deviation of the sampling distribution is the standard error itself, not s. The variance of the sampling distribution would be the square of the standard error, not s. The standard deviation of the sample is exactly what s represents.