Calculate standard deviation in excel

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

STDEV(number1,[number2],…)

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.

Remarks

• 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.

Data
Strength
1345
1301
1368
1322
1310
1370
1318
1350
1303
1299
Formula	Description (Result)	Result
=STDEV(A3:A12)	Standard deviation of breaking strength (27.46392)	27.46392

Excel is used extensively for statistics and data analysis. Standard deviation is something that is used quite often in statistical calculations.

In this tutorial, I will show you how to calculate the standard deviation in Excel (using simple formulas)

But before getting into, let me quickly give you a brief overview of what standard deviation is and how it’s used.

What is Standard Deviation?

A standard deviation value would tell you how much the data set deviates from the mean of the data set.

For example, suppose you have a group of 50 people, and you are recording their weight (in kgs).

In this data set, the average weight is 60 kg, and the standard deviation is 4 kg. It means that most of the people’s weight is within 4 kg of the average weight (which would be 56-64 kg).

Now let’s interpret the standard deviation value:

• A lower value indicates that the data points tend to be closer to the average (mean) value.
• A higher value indicates that there is widespread variation in the data points. This can also be a case when there are many outliers in the data set.

Calculating Standard Deviation in Excel

While it’s easy to calculate the standard deviation, you need to know which formula to use in Excel.

There are six standard deviation formulas in Excel (eight if you consider database functions as well).

These six formulas can be divided into two groups:

1. Calculating the sample standard deviation: The formulas in this category are STDEV.S, STDEVA, and STDEV
2. Calculating the standard deviation for an entire population: The formulas in this category are STDEV.P, STDEVPA, and STDEVP

In almost all of the cases, you will use standard deviation for a sample.

Again in layman terms, you use the term ‘population’ when you want to consider all the datasets in the entire population. On the other hand, you use term ‘sample’ when using a population is not possible (or it’s unrealistic to do so). In such a case, you pick a sample from the population.

You can use the sample data to calculate the standard deviation and infer for the entire population. You can read a great explanation of it here (read the first response).

So. this narrows down the number of formulas to three (STDEV.S, STDEVA, and STDEV function)

Now let’s understand these three formulas:

• STDEV.S – Use this when your data is numeric. It ignores the text and logical values.
• STDEVA – Use this when you want to include text and logical values in the calculation (along with numbers). Text and FALSE are taken as 0 and TRUE is taken as 1.
• STDEV – STDEV.S was introduced in Excel 2010. Before it, the STDEV function was used. It is still included for compatibility with prior versions.

So, you can safely assume that in most of the cases, you would have to use STDEV.S function (or STDEV function if you’re using Excel 2007 or prior versions).

So now let’s see how to use it in Excel.

Using STDEV.S Function in Excel

As mentioned, STDEV.S function uses numerical values but ignores the text and logical values.

Here is the syntax of STDEV.S function:

STDEV.S(number1,[number2],…)

• Number1 – This is a mandatory argument in the formula. The first number argument corresponds to the first element of the sample of a population. You can also use a named range, single array, or a reference to an array instead of arguments separated by commas.
• Number2, … [Optional argument in the formula] You can use up to 254 additional arguments. These can refer to a data point, a named range, a single array, or a reference to an array.

Now, let’s have a look at a simple example where we calculate the standard deviation.

Example – Calculating the Standard Deviation for Weight Data

Suppose you have a data set as shown below:

To calculate the standard deviation using this data set, use the following formula:

=STDEV.S(A2:A10)

In case you’re using Excel 2007 or prior versions, you will not have the STDEV.S function. In that case, you can use the below formula:

=STDEV(D2:D10)

The above formula returns the value of 2.81, which indicates that most of the people in the group would be within the weight range 69.2-2.81 and 69.2+2.81.

Note that when I say ‘most of the people’, it refers to the normal distribution of the sample (that is 68% of the sample population is within one standard deviation from the mean).

Also, note that this is a very small sample set. In reality, you may have to do this for a bigger sample data set where you can observe normal distribution better.

Hope you found this Excel tutorial useful.

You May Also Like the Following Excel Tutorials:

• Calculating Weighted Average in Excel.
• Calculating CAGR in Excel.
• Calculate and Format Percentages in Excel.
• Calculate Age in Excel using Formulas.
• Creating a Bell Curve in Excel.
• Calculating Compound Interest in Excel.
• How to Calculate Square Root in Excel
• Calculate the Coefficient of Variation (CV) in Excel
• How to Calculate Correlation Coefficient in Excel
• How to Get Descriptive Statistics in Excel?

What is Standard Deviation? | STDEV.P | STDEV.S | Variance

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).

6. Take the square root.

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.

2. Take the square root.

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.