Standard Deviation in Google Sheets (Sample & Population)

Standard deviation is one of the most common ways to measure the spread of values in a dataset.

There are two different types of standard deviations you can calculate, depending on the type of data you’re working with.

1. Population standard deviation

You should calculate the population standard deviation when the dataset you’re working with represents an entire population, i.e. every value that you’re interested in.

The formula to calculate a population standard deviation, denoted as σ, is:

σ = √Σ(x_i – μ)² / N

where:

• Σ: A symbol that means “sum”
• x_i: The i^th value in a dataset
• μ: The population mean
• N: The population size

2. Sample standard deviation

You should calculate the sample standard deviation when the dataset you’re working with represents a a sample taken from a larger population of interest.

The formula to calculate a sample standard deviation, denoted as s, is:

s = √Σ(x_i – x̄)² / (n – 1)

where:

• Σ: A symbol that means “sum”
• x_i: The i^th value in a dataset
• x̄: The sample mean
• n: The sample size

The following examples show how to calculate the sample and population standard deviation in Google Sheets.

Example 1: Calculating Sample Standard Deviation in Google Sheets

Suppose a biologist wants to summarize the standard deviation of the weight of a particular species of turtles so she collects a simple random sample of 20 turtles from the population.

Since she’s using a sample to estimate the standard deviation of the population, she can calculate the sample standard deviation.

The following screenshot shows how to use the STDEV.S() function to calculate the sample standard deviation:

The sample standard deviation turns out to be 11.91.

Note that STDEV() will also return the sample standard deviation.

Example 2: Calculating Population Standard Deviation in Google Sheets

Suppose a basketball coach wants to summarize the standard deviation of points scored by the 12 players on his team.

Since he is only interested in the points scored by his players and not any other players on any other team, he can calculate the population standard deviation.

The following screenshot shows how to use the STDEV.P() function to calculate the population standard deviation:

The population standard deviation turns out to be 7.331.

Additional Resources

The following tutorials offer additional information about standard deviation:

• Population vs. Sample Standard Deviation: When to Use Each
• Coefficient of Variation vs. Standard Deviation: The Difference
• Why is Standard Deviation Important?

The following tutorials explain how to calculate other measures of spread in Google Sheets:

• How to Calculate Interquartile Range in Google Sheets
• How to Calculate Coefficient of Variation in Google Sheets