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.

Overview of Calculation of Standard Deviation of Probability Distribution


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.

Dataset to Calculate Standard Deviation of Probability Distribution


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:

σ = √{Σ(xi-μ)^2 * P(xi)}

Steps:

  • First, I created a column of (xi-μ)^2 * P(xi), a cell to calculate the Total of all the values of (xi-μ)^2 * P(xi). In addition, I have added two rows of μ and σ = √{Σ(xi-μ)^2 * P(xi)}.

Creating Outline to Use Generic Formula to Calculate Standard Deviation of Probability Distribution

  • Select cell D14.
  • I will calculate μ 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)

Calculating μ(Mean) With the Formula

  • Select cell D5.
  • To calculate the (xi-μ)^2 * P(xi), I will subtract the μ 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

Calculating (xi-μ)^2 * P(xi) with Formula

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

Autofill the Formulas for (xi-μ)^2 * P(xi)

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

Calculating the total of (xi-μ)^2 * P(xi)

  • Select cell D15.
  • Type the following formula of cell references to calculate σ = √{Σ(xi-μ)^2 * P(xi)}:
=(D12)^(1/2)

Calculating Standard Deviation of Probability Distribution

The final value is the Standard Deviation of Probability Distribution.

Read More: How to Calculate Variance of Probability Distribution in Excel


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, Σ(xi-μ)^2 * P(xi), and Deviation. Here, St. Deviation is a short form used for Standard Deviation.

Creating Outline to Use SUMPRODUCT and SQRT Functions to Calculate Standard Deviation of Probability Distribution

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

Formula Breakdown

  • SUMPRODUCT(B5:B11, C5:C11) → 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 → 225.3.

Calculating Mean by Using SUMPRODUCT Function

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

How Does This Formula Work?

  • SUMPRODUCT((B5:B11-C13)^2, C5:C11) 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 → 176135.6916.

Calculating Variance by Using SUMPRODUCT Function

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

Formula Breakdown

  • SQRT(C14) → becomes
    • SQRT(176135.6916) → The SQRT function will square root the given value of Σ(xi-μ)^2 * P(xi).
      • Output → 419.6852292.

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

Calculating Standard Deviation of Probability distribution by Using SQRT Function

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

Read More: How to Use Continuous Probability Distribution in Excel


Practice Section

On the right side of each worksheet, you will find a practice section to practice on your own.

Practice Section for Standard Deviation of Probability


Download Practice Workbook

You can download the practice workbook here.


Conclusion

In this article, you will be able to learn how to calculate the Standard Deviation of probability distribution in Excel. You can suggest your thoughts about this article in the comment section below.


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Rabeya Islam
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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