How To Calculate The Standard Deviation Using Excel

This calculator helps you find the standard deviation of a set of numbers, similar to how you would calculate standard deviation using Excel functions like STDEV.S or STDEV.P. Enter your data below.

Data Point (xi)	Difference from Mean (xi – x̄)	Squared Difference (xi – x̄)²
Sum:	~0

Table showing individual data points and their contribution to variance.

What is Standard Deviation?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.

In finance, standard deviation is often used as a measure of volatility or risk. For example, the standard deviation of the daily or monthly returns of an investment (like a stock or mutual fund) is a measure of its volatility.

Excel provides functions to calculate standard deviation: STDEV.S for a sample and STDEV.P for an entire population. This calculator can help you understand the numbers behind these Excel functions.

Who should use it?

Students, researchers, analysts, investors, and anyone working with data who needs to understand its spread or variability can benefit from calculating standard deviation. If you are learning how to calculate standard deviation using Excel, this tool and guide are for you.

Common Misconceptions

A common misconception is that a high standard deviation is always “bad.” It simply means the data is more spread out. In some contexts (like diverse survey responses), this spread is natural and expected, while in others (like manufacturing tolerances), a low standard deviation is desired.

Standard Deviation Formula and Mathematical Explanation

There are two main formulas for standard deviation, depending on whether you are working with data from an entire population or a sample of a population:

1. Population Standard Deviation (σ)

If your data represents the entire population of interest, you use the population standard deviation formula:

σ = √[ Σ(xi – μ)² / N ]

Where:

• σ (sigma) is the population standard deviation.
• Σ (sigma) is the summation symbol, meaning “sum of”.
• xi are the individual data points.
• μ (mu) is the population mean.
• N is the total number of data points in the population.

In Excel, you use the STDEV.P function to calculate standard deviation using Excel for a population.

2. Sample Standard Deviation (s)

If your data is a sample taken from a larger population, you use the sample standard deviation formula, which provides an unbiased estimate of the population standard deviation:

s = √[ Σ(xi – x̄)² / (n – 1) ]

Where:

• s is the sample standard deviation.
• xi are the individual data points in the sample.
• x̄ (x-bar) is the sample mean.
• n is the number of data points in the sample.
• (n – 1) is used in the denominator (Bessel’s correction) to provide a more accurate estimate of the population standard deviation from the sample.

In Excel, you use the STDEV.S function to calculate standard deviation using Excel for a sample.

Variables Table

Variable	Meaning	Unit	Typical Range
xi	Individual data point	Same as data	Varies with data
μ or x̄	Mean (average) of the data	Same as data	Varies with data
N or n	Number of data points	Count (unitless)	≥1 (for sample SD, ≥2)
σ or s	Standard Deviation	Same as data	≥0
Σ(xi – μ)² or Σ(xi – x̄)²	Sum of Squared Differences from the Mean	Square of data units	≥0

Variables used in standard deviation formulas.

Practical Examples (Real-World Use Cases)

Example 1: Test Scores

A teacher has the following scores from a small quiz: 70, 75, 80, 85, 90. They want to calculate the sample standard deviation to understand the spread of scores.

Data: 70, 75, 80, 85, 90

1. Calculate the Mean (x̄): (70 + 75 + 80 + 85 + 90) / 5 = 400 / 5 = 80
2. Calculate Differences from Mean: -10, -5, 0, 5, 10
3. Square the Differences: 100, 25, 0, 25, 100
4. Sum of Squared Differences: 100 + 25 + 0 + 25 + 100 = 250
5. Divide by n-1: 250 / (5 – 1) = 250 / 4 = 62.5 (This is the variance)
6. Take the Square Root: √62.5 ≈ 7.91

The sample standard deviation is approximately 7.91. Using Excel, =STDEV.S(70, 75, 80, 85, 90) would give the same result.

Example 2: Daily Sales

A small shop records daily sales for a week: 150, 165, 140, 170, 155, 160, 145. We want to find the population standard deviation assuming this week represents all sales data of interest.

Data: 150, 165, 140, 170, 155, 160, 145 (N=7)

1. Mean (μ): (150+165+140+170+155+160+145) / 7 = 1085 / 7 ≈ 155
2. Squared Differences from Mean (approx): (150-155)²=25, (165-155)²=100, (140-155)²=225, (170-155)²=225, (155-155)²=0, (160-155)²=25, (145-155)²=100
3. Sum of Squared Differences: 25 + 100 + 225 + 225 + 0 + 25 + 100 = 700
4. Divide by N: 700 / 7 = 100 (Variance)
5. Square Root: √100 = 10

The population standard deviation is 10. Using Excel, =STDEV.P(150, 165, 140, 170, 155, 160, 145) would give 10.

How to Use This Standard Deviation in Excel Calculator

1. Enter Data: Type your numerical data points into the “Enter Data (comma-separated)” text area. Make sure values are separated by commas (e.g., 23, 45, 61, 33).
2. Select Type: Choose whether you want to calculate the “Sample (STDEV.S, n-1)” or “Population (STDEV.P, n)” standard deviation using the radio buttons. If you’re unsure, “Sample” is more common when analyzing data that is part of a larger group.
3. Calculate: Click the “Calculate” button or just finish typing. The results will update automatically if you just change input.
4. View Results: The calculator will display:
   • The Standard Deviation (primary result).
   • The Mean (average) of your data.
   • The Variance.
   • The Number of Data Points (N).
   • The Sum of Squares (SS).
   • An explanation of the formula used.
5. Examine Table & Chart: If data is valid, a table showing each data point, its difference from the mean, and the squared difference will appear, along with a chart visualizing the data.
6. Reset: Click “Reset” to clear the inputs and results.
7. Copy Results: Click “Copy Results” to copy the main outputs to your clipboard.

This tool mirrors what you would get if you were to calculate standard deviation using Excel‘s built-in functions.

Key Factors That Affect Standard Deviation Results

• Spread of Data: The more spread out the data points are from the mean, the higher the standard deviation.
• Outliers: Extreme values (outliers) can significantly increase the standard deviation because their squared differences from the mean are large.
• Number of Data Points (for Sample SD): The (n-1) in the denominator for sample standard deviation means that with very small samples, the standard deviation can be more sensitive to changes in data.
• Scale of Data: If you multiply all your data points by a constant, the standard deviation will also be multiplied by that constant. For example, if you change units from meters to centimeters, the standard deviation value will increase.
• Data Entry Errors: Incorrectly entered data points can drastically alter the standard deviation.
• Sample vs. Population Choice: Using the (n-1) denominator for samples gives a larger standard deviation than using ‘n’ for populations, especially with small ‘n’. Choosing the correct one is vital for correct interpretation when you calculate standard deviation using Excel or any tool.

Frequently Asked Questions (FAQ)

What’s the difference between sample and population standard deviation?

You use population standard deviation when your dataset includes every member of the entire group you are interested in. You use sample standard deviation when your dataset is a smaller sample taken from a larger population, and you want to estimate the population’s spread. The sample formula (dividing by n-1) gives a slightly larger, more conservative estimate.

How do I calculate standard deviation using Excel?

Excel has built-in functions: STDEV.S(range) for sample standard deviation and STDEV.P(range) for population standard deviation, where ‘range’ is the set of cells containing your data (e.g., A1:A10).

What does a high standard deviation mean?

A high standard deviation means the data points are widely spread out from the mean. There is high variability or dispersion.

What does a low standard deviation mean?

A low standard deviation means the data points are clustered closely around the mean. There is low variability.

Can standard deviation be negative?

No, standard deviation cannot be negative. It is calculated as the square root of variance (which is an average of squared values), so it is always non-negative (zero or positive).

What is variance?

Variance is the average of the squared differences from the Mean. Standard deviation is the square root of the variance, bringing the measure back into the original units of the data.

When should I use the STDEV.S function in Excel?

Use STDEV.S when your data is a sample of a larger population, and you want to estimate the standard deviation of that larger population based on your sample. This is the most common scenario when you calculate standard deviation using Excel in many fields.

When should I use the STDEV.P function in Excel?

Use STDEV.P when your data represents the entire population you are interested in (e.g., the test scores of ALL students in a particular class, and you are only interested in that class).