Probability distribution indicates a 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.

## Download Practice Workbook

You can download the practice workbook here.

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

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 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)}**.

- 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)`

- 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`

- 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-μ)^2 * P(xi)**cell:

`=D5+D6+D7+D8+D9+D10+D11`

- Select cell
**D15**. - Type the following formula of cell references to calculate
**σ = √{Σ(xi-μ)^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**,**Σ(xi-μ)^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) → 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**.

- 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**.

- Select cell
**C15**. - Then type the following formula to calculate
**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**.

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

## Practice Section

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

## Conclusion

In this article, you will be able to learn how to **Calculate the Standard Deviation of Probability Distribution** in Excel. Follow our **ExcelDemy** page for regular blogs related to Excel. You can suggest your thoughts about this article in the comment section below.