Standard deviation is a statistical measure that helps you understand how spread out the data points in a dataset are. It quantifies the amount of variation or uncertainty in a set of values.
Calculating standard deviation in Excel
Excel provides two functions for calculating standard deviation, each suited for a specific type of data analysis:
- STDEV.S: Calculates the standard deviation for a sample dataset. This function is used when your data represents a sample of the entire population.
- STDEV.P: Calculates the standard deviation for an entire population. This function is used when your data includes every member of the population.
Syntax:
- STDEV.S(number1, [number2], …)
- STDEV.P(number1, [number2], …)
Arguments:
- number1: Required. The first number in the range of data for which you want to calculate the standard deviation.
- number2, …: Optional. Additional numbers in the range of data for which you want to calculate the standard deviation.
Example:
To calculate the standard deviation for the sample dataset in cells A1 to A10, you would use the following formula: =STDEV.S(A1:A10)
To calculate the standard deviation for the population dataset in cells A1 to A10, you would use the following formula: =STDEV.P(A1:A10)
Using Non-Contiguous Ranges
You can also calculate standard deviation across non-contiguous cells by listing them separately:
=STDEV.S(A1:A5, C1:C5)
This approach is useful when your data is spread across multiple columns or when you want to exclude certain rows from your calculation.
Interpreting Standard Deviation:
The standard deviation is typically interpreted as follows:
- Low standard deviation: The data points are close to the mean, indicating that the data is relatively uniform.
- High standard deviation: The data points are spread out over a wide range, indicating that the data is more variable.
A high standard deviation indicates that the data is more variable, which can be useful for identifying outliers or anomalies. A low standard deviation indicates that the data is more uniform, which can be useful for making predictions.
Standard Deviation in Context: The 68-95-99.7 Rule
Understanding the normal distribution helps you interpret standard deviation more effectively. In a normal distribution:
- Approximately 68% of data points fall within one standard deviation of the mean
- Approximately 95% of data points fall within two standard deviations of the mean
- Approximately 99.7% of data points fall within three standard deviations of the mean
This rule helps you understand how unusual a particular data point is and whether it warrants further investigation.
High standard deviation doesn’t mean your data is “bad”—it just means it’s more variable. Whether this is good or bad depends on your context and what you’re measuring.
