# How to Find Standard Deviation of Probability Distribution in Excel

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Probability distribution indicates the probability of a variable depending on a certain value. While working on probability distribution, we must find out the standard deviation. In this tutorial, I will write about how to Calculate the Standard Deviation of Probability Distribution in Excel.

## How to Calculate Standard Deviation of Probability Distribution in Excel: 2 Simple Methods

I have a dataset of Probability Distribution, where the attributes are No. of New Students (X) and Probability of Admission P(X). Here, I will show the calculation of the Standard Deviation of Probability Distribution in both generic and function methods. For this tutorial, I used the Microsoft Excel 365 version.

### 1. Using Generic Formula to Calculate Standard Deviation of Probability Distribution

You can use generic formulas to calculate the Standard Deviation of the probability distribution. The formula of Standard Deviation is:

`Ïƒ = âˆš{Î£(xi-Î¼)^2 * P(xi)}`

Steps:

• First, I created a column of (xi-Î¼)^2 * P(xi), a cell to calculate the Total of all the values of (xi-Î¼)^2 * P(xi). In addition, I have added two rows of Î¼ and Ïƒ = âˆš{Î£(xi-Î¼)^2 * P(xi)}.

• Select cell D14.
• I will calculate Î¼ by multiplying each cell value of No. of New Students (X) with their respective cell value of Probability of Admission P(X) and then by adding up altogether.
`=(B5*C5)+(B6*C6)+(B7*C7)+(B8*C8)+(B9*C9)+(B10*C10)+(B11*C11)`

• Select cell D5.
• To calculate the (xi-Î¼)^2 * P(xi), I will subtract the Î¼ from each of the cells of No. of New Students (X) and then square it to multiply the value with each of the cells of Probability of Admission P(X).
`=(B5-\$C\$14)^2*C5`

• After that, I Filled other cells using the Autofill Feature.

• Select cell D12.
• Type the following formula of cell references, to sum up, the values of every (xi-Î¼)^2 * P(xi) cell:
`=D5+D6+D7+D8+D9+D10+D11`

• Select cell D15.
• Type the following formula of cell references to calculate Ïƒ = âˆš{Î£(xi-Î¼)^2 * P(xi)}:
`=(D12)^(1/2)`

The final value is the Standard Deviation of Probability Distribution.

### 2. Applying SUMPRODUCT, SQRT Functions to Calculate Standard Deviation of Probability Distribution

You can also use SUMPRODUCT and SQRT functions to calculate the Standard Deviation of Probability Distribution.

Steps:

• First, create rows for Mean, Î£(xi-Î¼)^2 * P(xi), and Deviation. Here, St. Deviation is a short form used for Standard Deviation.

• Select cell C13.
• Type the following formula to calculate the Mean:
`=SUMPRODUCT(B5:B11, C5:C11)`

Formula Breakdown

• SUMPRODUCT(B5:B11, C5:C11) â†’ The SUMPRODUCT function will add values after multiplying each cell value of No. of New Students (X) with the respective cell value of Probability of Admission P(X).
• B5:B11 is the cell range of the No. of New Students (X) column.
• C5:C11 is the cell range of the Probability of Admission P(X)
• Output â†’ 225.3.

• Select cell C14.
• Type the following formula to calculate Î£(xi-Î¼)^2 * P(xi):
`=SUMPRODUCT((B5:B11-C13)^2, C5:C11)`

How Does This Formula Work?

• SUMPRODUCT((B5:B11-C13)^2, C5:C11) â†’ The SUMPRODUCT function will add values after multiplying each cell of the given cell ranges.
• (B5:B11-C13)^2 is for subtracting Mean from each of the cell values from No. of New Students (X) and square the value afterward.
• C5:C11 is the total cell range of the Probability of Admission P(X)
• Output â†’ 176135.6916.

• Select cell C15.
• Then type the following formula to calculate St. Deviation:
`=SQRT(C14)`

Formula Breakdown

• SQRT(C14) â†’ becomes
• SQRT(176135.6916) â†’ The SQRT function will square root the given value of Î£(xi-Î¼)^2 * P(xi).
• Output â†’ 419.6852292.

Now, we have the standard deviation of probability distribution in cell C15.

Finally, the value you get is the Standard Deviation of Probability Distribution.

## Practice Section

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Rabeya Islam

Rabeya Islam, BSc, Computer Science and Engineering, East West University, Bangladesh, has been working with the SOFTEKO for more than one and half years. She has written some articles for ExcelDemy. Currently, she is working as the team leader, oversees the day-to-day work, and leads the SQA team Excel Extensions project. She has built the workflow and the structure of the extension testing for the team. Her work and learning interests vary from Microsoft Office Suites, VBA, and... Read Full Bio

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