The standard error of the mean is a way to measure how spread out values are in a dataset. It is calculated as:
Standard error = s / √n
where:
- s: sample standard deviation
- n: sample size
We can calculate the standard error of the mean for a given dataset in Google Sheets by using the following formula:
=STDEV.S(range of values) / SQRT(COUNT(range of values))
The following example demonstrates how to use this formula.
Example: Standard Error in Google Sheets
Suppose we have the following dataset:
The following formula shows how to calculate the standard error of the mean for this dataset:
The standard error of the mean turns out to be 2.0014.
How to Interpret the Standard Error of the Mean
The standard error of the mean is a measure of how spread out values are around the mean. There are two things to keep in mind when interpreting the standard error of the mean:
1. The larger the standard error of the mean, the more spread out values are around the mean in a dataset.
To illustrate this, consider if we change the last value in the previous dataset to a much larger number:
Notice how the standard error jumps from 2.0014 to 6.9783. This tells us that the values in this dataset are more spread out around the mean compared to the previous dataset.
2. As the sample size increases, the standard error of the mean tends to decrease.
To illustrate this, consider the standard error of the mean for the following two datasets:
The second dataset is simply the first dataset repeated twice. Thus, the two datasets have the same mean but the second dataset has a larger sample size so it has a smaller standard error.