Excel Standard Deviation Formula

Formula Overview

The standard deviation in Excel can be calculated using the STDEV.P and STDEV.S functions.

• STDEV.P: Calculates the standard deviation for a population.
• STDEV.S: Calculates the standard deviation for a sample.

Syntax

1. Population Standard Deviation:

   • =STDEV.P(number1, [number2], ...)

2. Sample Standard Deviation:

   • =STDEV.S(number1, [number2], ...)

Parameters

• number1: The first number or range of cells to consider.
• number2: (optional) Additional numbers or ranges.

Example

Scenario

Assume you have a dataset of test scores in cells A1 through A10. You want to calculate both the population standard deviation and the sample standard deviation of these scores.

Population Standard Deviation

To calculate the population standard deviation:

=STDEV.P(A1:A10)

Sample Standard Deviation

To calculate the sample standard deviation:

=STDEV.S(A1:A10)

Explanation

• STDEV.P: This function considers all points in your dataset as a full population. It computes the standard deviation by taking the square root of the variance. This is useful when you have data reflecting the entire population.

• STDEV.S: This function estimates the standard deviation based on a sample of the population. It uses a slightly different formula by dividing by (n-1) (where (n) is the number of observations) rather than (n). This is beneficial when working with a subset of data, providing an unbiased estimate.

Practical Illustration

Imagine the following test scores in Excel:

Steps:

1. Populate cells A1 through A10 with the test scores.
2. In cell B1, enter the formula =STDEV.P(A1:A10) for the population standard deviation.
3. In cell B2, enter the formula =STDEV.S(A1:A10) for the sample standard deviation.

Output:

• Cell B1 will display the population standard deviation based on all scores.
• Cell B2 will display the sample standard deviation.

Conclusion

The choice between STDEV.P and STDEV.S depends on whether your dataset represents the entire population or just a sample. Understanding and applying these formulas will enhance your data analysis proficiency in Excel. For further learning and advanced techniques, consider exploring the Enterprise DNA Platform.