Standard Deviation Calculator (for Excel Users)

Calculate standard deviation using the exact same formulas as Microsoft Excel’s STDEV.S and STDEV.P functions.

Mean (Average)

Variance

Count (n)

A visual representation of your data points in relation to the mean.

What is calculating standard deviation using Microsoft Excel?

Calculating standard deviation is a fundamental statistical method to measure the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (or average) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Microsoft Excel is a powerful tool that simplifies this calculation with its built-in functions.

For anyone working with data in Excel, understanding standard deviation is crucial for interpreting data variability. Excel provides two primary functions for this purpose: STDEV.S for a sample of data, and STDEV.P for an entire population. This calculator mirrors those functions, helping you understand how Excel computes these values and allowing you to perform the same calculations online.

Standard Deviation Formula and Explanation

The core of the calculation differs slightly depending on whether you are analyzing a full population or just a sample of it.

Sample Standard Deviation (STDEV.S)

This is the most common scenario. When your data is a sample of a larger group, you use the “n-1” method to calculate the variance, which corrects for the bias of using a sample.

Formula: s = √[ Σ(xᵢ - x̄)² / (n - 1) ]

Population Standard Deviation (STDEV.P)

If your dataset includes every member of the group you are interested in, you are working with a population. In this case, the denominator for the variance is simply the size of the population (n).

Formula: σ = √[ Σ(xᵢ - µ)² / N ]

Description of formula variables

Variable	Meaning	Unit	Typical Range
s or σ	Standard Deviation	Same as input data	0 to ∞
x̄ or µ	Mean (Average) of the data set	Same as input data	Varies with data
x̅	Each individual data point	Same as input data	Varies with data
n or N	The total count of data points	Unitless	2 to ∞
Σ	Summation (adding all values together)	Unitless	N/A

Practical Examples

Example 1: Calculating Sample Standard Deviation

Imagine you are a teacher and you’ve graded a pop quiz for a sample of 5 students. Their scores are 70, 85, 88, 92, and 65.

• Inputs: 70, 85, 88, 92, 65
• Calculation Type: Sample (STDEV.S)
• Steps:
  1. Calculate the mean: (70 + 85 + 88 + 92 + 65) / 5 = 80
  2. Calculate the squared differences from the mean: (70-80)²=100, (85-80)²=25, (88-80)²=64, (92-80)²=144, (65-80)²=225
  3. Sum the squared differences: 100 + 25 + 64 + 144 + 225 = 558
  4. Divide by n-1: 558 / 4 = 139.5 (This is the variance)
  5. Take the square root: √139.5 ≈ 11.81
• Result: The sample standard deviation is approximately 11.81. In Excel, `=STDEV.S(70, 85, 88, 92, 65)` would give the same result.

Example 2: How to Calculate in Microsoft Excel

Let’s say you have monthly sales data for a full year and want to find the population standard deviation. This is a population because it includes all the data for the period you’re interested in.

1. Enter Your Data: Type your 12 monthly sales figures into an Excel column, for instance, from cell A1 to A12.
2. Choose a Result Cell: Click on an empty cell where you want the result to appear.
3. Enter the Formula: Type `=STDEV.P(A1:A12)` into the cell.
4. Press Enter: Excel will immediately calculate and display the population standard deviation for your sales data.

Using the STDEV.S formula follows the exact same process, you would just type `=STDEV.S(A1:A12)` instead. For more complex scenarios, you might want to look into an Advanced Excel Course.

How to Use This Standard Deviation Calculator

1. Enter Your Data: Type or paste the numbers from your data set into the “Data Set” text area. Ensure all numbers are separated by a comma.
2. Select Calculation Type: Choose between ‘Sample Standard Deviation (STDEV.S)’ if your data represents a sample of a larger group, or ‘Population Standard Deviation (STDEV.P)’ if you have data for the entire group. The default is Sample, which is the most common use case.
3. Calculate: Click the “Calculate” button.
4. Interpret Results: The calculator will display the main result (Standard Deviation) along with key intermediate values like the mean, variance, and the count of your data points. A bar chart will also show the distribution of your data relative to the mean.

Key Factors That Affect Standard Deviation

• Outliers: Extremely high or low values in the data set can significantly increase the standard deviation because they are far from the mean.
• Data Spread: The more spread out the data points are, the higher the standard deviation. Data clustered tightly around the mean results in a low standard deviation.
• Sample Size (n): For sample standard deviation, a smaller sample size (n) leads to a larger denominator (n-1 relative to n), which can impact the result. As the sample size increases, the difference between sample and population standard deviation becomes smaller.
• Units of Measurement: The standard deviation is expressed in the same units as the original data. Changing the unit (e.g., from feet to inches) will change the standard deviation value.
• Data Distribution: While not a direct factor in the calculation, the shape of the data’s distribution (e.g., normal, skewed) provides context for interpreting the standard deviation.
• Mean Value: Since every calculation is based on the distance from the mean, any change in the mean (e.g., by adding or removing data points) will affect the standard deviation. Check out our Mean, Median, & Mode Calculator for more on this topic.

Frequently Asked Questions (FAQ)

What’s the main difference between STDEV.S and STDEV.P?

STDEV.S is used when your data is a *sample* of a larger population. STDEV.P is used when your data represents the *entire* population. The formula for STDEV.S divides by n-1, while STDEV.P divides by N.

When should I use sample vs. population standard deviation?

In most real-world scenarios, you use sample standard deviation (STDEV.S) because it’s rare to have data for an entire population. For example, if you measure the height of 100 people to estimate the average height in a country, that’s a sample. If you measure the height of every student in a single classroom, that’s a population.

What does a standard deviation of 0 mean?

A standard deviation of 0 means that all values in the data set are identical. There is no variation or spread, so all points are equal to the mean.

Can I calculate standard deviation with non-numeric text in Excel?

No. The STDEV.S and STDEV.P functions in Excel ignore text and logical values. This calculator does the same to accurately mimic Excel’s behavior.

Is a lower standard deviation better?

Not necessarily. “Better” depends on the context. In manufacturing, a low standard deviation for a product’s size is good (consistency). In investing, a low standard deviation means low risk but potentially low returns.

How do outliers affect standard deviation?

Outliers have a significant impact, pulling the mean towards them and increasing the squared differences, which inflates the standard deviation. This can sometimes give a misleading picture of the data’s overall variability.

Why does the sample formula divide by n-1?

Dividing by n-1 (known as Bessel’s correction) provides an unbiased estimate of the population variance. Because a sample is smaller than the full population, its variance is likely to be slightly lower. The n-1 adjustment compensates for this.

What’s the relationship between variance and standard deviation?

The standard deviation is simply the square root of the variance. Variance is measured in squared units (e.g., dollars squared), which is hard to interpret. Taking the square root brings the measure back to the original units (e.g., dollars), making standard deviation more intuitive.