Sample standard deviation excel

The standard deviation shows the variability of the data values from the mean (average). In Excel, the STDEV and STDEV.S calculate sample standard deviation while STDEVP and STDEV.P calculate population standard deviation. STDEV is available in Excel 2007 and the previous versions. However, STDEV.P and STDEV.S are only available in Excel 2010 and subsequent versions.

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Standard Deviation Formulas in Excel

In excel, there are eight formulas to calculate the standard deviation. These are grouped under sample and population.

The functions STDEV.S, STDEVA, STDEV, DSTDEV are under sample and STDEV.P, STDEVP, STDEVPA, DSTDEVP are under population.

The Syntax of STDEV.S Function

The syntax of the function is stated as follows:

The function accepts the following arguments:

• Number 1: This is the first value of the sample data. It can be expressed as a range.
• Number 2: This is the second value of the sample data.

“Number 1” is mandatory and “number 2” is an optional argument.

Note 1: If the entire sample data is entered as a range, the “number 2” argument becomes optional.

Note 2: The sample standard deviation formula works correctly when the supplied arguments contain at least two numeric values. Otherwise, it returns the “#DIV/0!” error.

The Population vs. Sample

The population and sample are defined as follows:

• The population refers to the whole data set.
• A sample is a subset of the data set. A sample of the population is taken when it is difficult to use the complete data set.

Note: The sample standard deviation helps make conclusions for the population.

The STDEV.S and STDEVA Functions

The two functions are explained as follows:

• The STDEV.S function calculates the standard deviationStandard deviation (SD) is a popular statistical tool represented by the Greek letter ‘σ’ to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data’s reliability.read more using the numerical values. It ignores the text values. The “S” of the function represents the sample data set.
• The STDEVA function calculates the standard deviation by counting the text values as zero. The logical value “false” is counted as 0 and “true” is counted as 1.

Note: The STDEV.S is available in Excel 2010 and the subsequent versions.

Calculating Standard Deviation in Excel

#1 – Calculate Population Standard Deviation in Excel

Let us consider an example to understand the concept of standard deviation in Excel.

The following are the employee scores of an organization. They indicate the skill levels of the employees.

We want to calculate the standard deviation of the given data set.

#2– Calculate Sample Standard Deviation in Excel

Let us consider an example to understand the working of the STDEV.S function.

The following table shows the heights of different goats. The height is measured from the shoulder level and is denoted in millimeters.

You can download this Standard Deviation Excel Template here – Standard Deviation Excel Template

Step 1: Calculate the mean of the given data. The output is 394.

Step 2: Apply STDEV.S to the range B2:B6. The output is 165.

Conclusion: The standard deviation of the height of the goats is 165. This indicates that the usual heights are within the range of 229 and 559 millimeters.

In other words, the heights are on either side of the mean, i.e., 394–165=229 and 394+165=559.

Frequently Asked Questions

Recommended Articles

This has been a guide to standard deviation in Excel. Here we discuss how to calculate standard deviation in excel using formula and examples. You may also look at these useful functions in Excel –

• Quartile DeviationQuartile deviation is based on the difference between the first quartile and the third quartile in the frequency distribution and the difference is also known as the interquartile range, the difference divided by two is known as quartile deviation or semi interquartile range.read more
• Sample Standard Deviation FormulaSample standard deviation refers to the statistical metric that is used to measure the extent by which a random variable diverges from the mean of the sample.read more
• Standard Deviation Graph in ExcelThe standard deviation is a metric that calculates how values change when compared to or in relation to the mean or average value. Both deviations are represented in a standard deviation graph, with one being positive on the right and the other being negative on the left.read more
• QUARTILE Function in Excel

STDEV function

Estimates standard deviation based on a sample. The standard deviation is a measure of how widely values are dispersed from the average value (the mean).

Important: This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

For more information about the new function, see STDEV.S function.

Syntax

The STDEV function syntax has the following arguments:

Number1 Required. The first number argument corresponding to a sample of a population.

Number2, . Optional. Number arguments 2 to 255 corresponding to a sample of a population. You can also use a single array or a reference to an array instead of arguments separated by commas.

STDEV assumes that its arguments are a sample of the population. If your data represents the entire population, then compute the standard deviation using STDEVP.

The standard deviation is calculated using the «n-1» method.

Arguments can either be numbers or names, arrays, or references that contain numbers.

Logical values and text representations of numbers that you type directly into the list of arguments are counted.

If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are ignored.

Arguments that are error values or text that cannot be translated into numbers cause errors.

If you want to include logical values and text representations of numbers in a reference as part of the calculation, use the STDEVA function.

STDEV uses the following formula:

where x is the sample mean AVERAGE(number1,number2,…) and n is the sample size.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

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STDEV.S function

Estimates standard deviation based on a sample (ignores logical values and text in the sample).

The standard deviation is a measure of how widely values are dispersed from the average value (the mean).

Syntax

The STDEV.S function syntax has the following arguments:

Number1 Required. The first number argument corresponding to a sample of a population. You can also use a single array or a reference to an array instead of arguments separated by commas.

Number2, . Optional. Number arguments 2 to 254 corresponding to a sample of a population. You can also use a single array or a reference to an array instead of arguments separated by commas.

STDEV.S assumes that its arguments are a sample of the population. If your data represents the entire population, then compute the standard deviation using STDEV.P.

The standard deviation is calculated using the «n-1» method.

Arguments can either be numbers or names, arrays, or references that contain numbers.

Logical values and text representations of numbers that you type directly into the list of arguments are counted.

If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are ignored.

Arguments that are error values or text that cannot be translated into numbers cause errors.

If you want to include logical values and text representations of numbers in a reference as part of the calculation, use the STDEVA function.

STDEV.S uses the following formula:

where x is the sample mean AVERAGE(number1,number2,…) and n is the sample size.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

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Standard Deviation in Excel

What is Standard Deviation in Excel?

The standard deviation shows the variability of the data values from the mean (average). In Excel, the STDEV and STDEV.S calculate sample standard deviation while STDEVP and STDEV.P calculate population standard deviation. STDEV is available in Excel 2007 and the previous versions. However, STDEV.P and STDEV.S are only available in Excel 2010 and subsequent versions.

You are free to use this image on your website, templates, etc., Please provide us with an attribution link How to Provide Attribution? Article Link to be Hyperlinked
For eg:
Source: Standard Deviation in Excel (wallstreetmojo.com)

Table of contents

Standard Deviation Formulas in Excel

In excel, there are eight formulas to calculate the standard deviation. These are grouped under sample and population.

The functions STDEV.S, STDEVA, STDEV, DSTDEV are under sample and STDEV.P, STDEVP, STDEVPA, DSTDEVP are under population.

The Syntax of STDEV.S Function

The syntax of the function is stated as follows:

The function accepts the following arguments:

• Number 1: This is the first value of the sample data. It can be expressed as a range.
• Number 2: This is the second value of the sample data.

“Number 1” is mandatory and “number 2” is an optional argument.

Note 1: If the entire sample data is entered as a range, the “number 2” argument becomes optional.

Note 2: The sample standard deviation formula works correctly when the supplied arguments contain at least two numeric values. Otherwise, it returns the “#DIV/0!” error.

The Population vs. Sample

The population and sample are defined as follows:

• The population refers to the whole data set.
• A sample is a subset of the data set. A sample of the population is taken when it is difficult to use the complete data set.

Note: The sample standard deviation helps make conclusions for the population.

The STDEV.S and STDEVA Functions

The two functions are explained as follows:

• The STDEV.S function calculates the standard deviationStandard DeviationStandard deviation (SD) is a popular statistical tool represented by the Greek letter ‘σ’ to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data’s reliability.read more using the numerical values. It ignores the text values. The “S” of the function represents the sample data set.
• The STDEVA function calculates the standard deviation by counting the text values as zero. The logical value “false” is counted as 0 and “true” is counted as 1.

Note: The STDEV.S is available in Excel 2010 and the subsequent versions.

Calculating Standard Deviation in Excel

#1 – Calculate Population Standard Deviation in Excel

Let us consider an example to understand the concept of standard deviation in Excel.

The following are the employee scores of an organization. They indicate the skill levels of the employees.

We want to calculate the standard deviation of the given data set.

The steps to calculate standard deviation in Excel are listed as follows:

Calculate the mean (average) of the data.

The output 55.2 signifies the average employee score.

Calculate the population variance. It is the difference of each score from the mean. The results are summed as shown in the following image.

Variance =

Variance =

The population variance is 3.36.

Calculate the standard deviation. It is the square root of the variance.

Conclusion: The standard deviation is 1.83. This indicates that the employee scores range from 53.37 to 57.03.

#2– Calculate Sample Standard Deviation in Excel

Let us consider an example to understand the working of the STDEV.S function.

The following table shows the heights of different goats. The height is measured from the shoulder level and is denoted in millimeters.

Step 1: Calculate the mean of the given data. The output is 394.

Step 2: Apply STDEV.S to the range B2:B6. The output is 165.

Conclusion: The standard deviation of the height of the goats is 165. This indicates that the usual heights are within the range of 229 and 559 millimeters.

In other words, the heights are on either side of the mean, i.e., 394–165=229 and 394+165=559.

Frequently Asked Questions

The standard deviation measures the dispersion of a given set of values from the mean. It shows the fluctuation of data values. A low standard deviation indicates lower variability and greater accuracy of the mean. On the other hand, a high standard deviation indicates higher variation and lesser reliability of the mean.

While investing, the standard deviation of the returns is evaluated to assess the volatility of a stock. In Excel, the STDEV and STDEV.S calculate sample standard deviation while STDEVP and STDEV.P calculate population standard deviation.

To select the appropriate standard deviation formula, the following points must be considered:
• The standard deviation is being calculated for a population or sample.
• The type of values of the data set. These values can be numerical, logical or textual.
• The version of MS Excel which is being used currently.

The steps to create a standard deviation graph in Excel are listed as follows:
• Create a usual Excel chart with the help of the “charts” group under the Insert tab.
• Select the chart and click the plus (+) sign on the top-right corner.
• In “chart elements,” click the arrow of “error bars,” and select “standard deviation.”

The standard deviation bars for the data points are inserted within the chart.

Key Takeaways

• STDEV calculates the standard deviation of the sample data supplied as an argument.
• The standard deviation shows the variability of the data values from the mean (average).
• The lower the standard deviation, the closer the data points to the mean.
• The higher the standard deviation, the more scattered the data points from the mean.
• The population refers to the entire data set while a sample is a subset of this data.
• The STDEV.S function calculates the standard deviation using the numerical values only.
• The STDEV.S function accepts two arguments–“number 1” and “number 2” representing the first and the second value of the sample data respectively.

Recommended Articles

This has been a guide to standard deviation in Excel. Here we discuss how to calculate standard deviation in excel using formula and examples. You may also look at these useful functions in Excel –

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Standard Deviation

This page explains how to calculate the standard deviation based on the entire population using the STDEV.P function in Excel and how to estimate the standard deviation based on a sample using the STDEV.S function in Excel.

What is Standard Deviation?

Standard deviation is a number that tells you how far numbers are from their mean.

1. For example, the numbers below have a mean (average) of 10.

Explanation: the numbers are all the same which means there’s no variation. As a result, the numbers have a standard deviation of zero. The STDEV function is an old function. Microsoft Excel recommends using the new STEDV.S function which produces the exact same result.

2. The numbers below also have a mean (average) of 10.

Explanation: the numbers are close to the mean. As a result, the numbers have a low standard deviation.

3. The numbers below also have a mean (average) of 10.

Explanation: the numbers are spread out. As a result, the numbers have a high standard deviation.

STDEV.P

The STDEV.P function (the P stands for Population) in Excel calculates the standard deviation based on the entire population. For example, you’re teaching a group of 5 students. You have the test scores of all students. The entire population consists of 5 data points. The STDEV.P function uses the following formula:

In this example, x₁ = 5, x₂ = 1, x₃ = 4, x₄ = 6, x₅ = 9, μ = 5 (mean), N = 5 (number of data points).

1. Calculate the mean (μ).

2. For each number, calculate the distance to the mean.

3. For each number, square this distance.

4. Sum (∑) these values.

5. Divide by the number of data points (N = 5).

7. Fortunately, the STDEV.P function in Excel can execute all these steps for you.

STDEV.S

The STDEV.S function (the S stands for Sample) in Excel estimates the standard deviation based on a sample. For example, you’re teaching a large group of students. You only have the test scores of 5 students. The sample size equals 5. The STDEV.S function uses the following formula:

In this example, x₁=5, x₂=1, x₃=4, x₄=6, x₅=9 (same numbers as above), x̄=5 (sample mean), n=5 (sample size).

1. Repeat steps 1-5 above but at step 5 divide by n-1 instead of N.

3. Fortunately, the STDEV.S function in Excel can execute all these steps for you.

Note: why do we divide by n — 1 instead of by n when we estimate the standard deviation based on a sample? Bessel’s correction states that dividing by n-1 instead of by n gives a better estimation of the standard deviation.

Variance

Variance is the square of the standard deviation. It’s that simple. Sometimes it’s easier to use the variance when solving statistical problems.

1. The VAR.P function below calculates the variance based on the entire population.

Note: you already knew this answer (see step 5 under STDEV.P). Take the square root of this result to find the standard deviation based on the entire population.

2. The VAR.S function below estimates the variance based on a sample.

Note: you already knew this answer (see step 1 under STDEV.S). Take the square root of this result to find the standard deviation based on a sample.

3. VAR and VAR.S produce the exact same result.

Note: Microsoft Excel recommends using the new VAR.S function.

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