How to Calculate Relative Standard Deviation in Google Sheets


The relative standard deviation is a measure of the sample standard deviation relative to the sample mean for a given dataset.

It is calculated as:

Relative standard deviation = s / x * 100%

where:

  • s: sample standard deviation
  • x: sample mean

This metric gives us an idea of how closely observations are clustered around the mean.

For example, suppose the standard deviation of a dataset is 4. If the mean is 400, then the relative standard deviation is 4/400 * 100% = 1%. This means the observations are clustered tightly around the mean.

However, a dataset that has a standard deviation of 40 and a mean of 400 will have a relative standard deviation of 10%. This means the observations are much more spread out around the mean relative to the previous dataset.

To calculate the relative standard deviation of a dataset in Google Sheets, we can use the following syntax:

=STDEV.S(A2:A21) / AVERAGE(A2:A21)

This particular example calculates the relative standard deviation for the dataset in the range A2:A21.

The following example shows how to use this syntax in practice.

Example: How to Calculate Relative Standard Deviation in Google Sheets

Suppose we have the following dataset in Google Sheets:

Suppose that we would like to calculate the relative standard deviation for this dataset.

We can type the following formula into cell D1 to do so:

=STDEV.S(A2:A21) / AVERAGE(A2:A21)

The following screenshot shows how to use this formula in practice:

relative standard deviation in Google Sheets

The relative standard deviation turns out to be 0.5932.

This tells us that the standard deviation of the dataset is 59.32% of the size of the mean of the dataset.

This number is fairly large, which indicates that the values are spread out a lot around the sample mean.

If we have multiple datasets, we can use the same formula to calculate the relative standard deviation (RSD) for each dataset and compare the RSD values across the datasets.

Additional Resources

The following tutorials explain how to perform other common tasks in Google Sheets:

How to Calculate the Mean Absolute Deviation in Google Sheets
How to Calculate Standard Deviation IF in Google Sheets
How to Calculate 2 Standard Deviations in Google Sheets

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