Statistical Inference

Standard Deviation of the Mean

The standard deviation of the mean (often called the standard error) is a measure of the variation in means of repeated samples. It is defined as the standard deviation divided by the square root of the sample size:

To calculate the standard deviation of the mean, do the following:

1. Calculate the standard deviation (s).
2. Calculate the square root of the sample size (n).
3. Divide the standard deviation by result of step 2.

Since we already calculated the standard deviation in the previous lesson, let's use that data to determine the standard deviation of the mean. Let's follow the steps:

1. The standard deviation is 18.4 (from the previous example).
2. The sample size is 16. The square root of 16 is 4.
3. 18.4 / 4 = 4.6

Therefore, the standard deviation of the mean is 4.6.