### What Is Mean Deviation?

**Mean Deviation** is a statistical measure of variability. It is calculated as the average of the absolute deviations of the data from the mean.

### Arithmetic Formula to Calculate Mean Deviation

The mean deviation can be calculated as the mean deviation from the mean or the mean deviation from the median. If in your calculation the arithmetic mean is subtracted from the individual values then it is called the mean deviation from the mean. If the subtracted item is the median then it is called the mean deviation from the median. The formulas for calculating the mean deviation are given below.

**Mean Deviation from Mean**

Where,

**X**is each observation**μ**is the arithmetic mean**N**is the total number of observations

**Mean Deviation from Median**

Where,

**X**is each observation**M**is the Median of the observations**N**is the total number of observations

### What Is Standard Deviation?

**Standard Deviation** is a statistical measure of dispersion, or how spread out data is. It is calculated as the square root of the variance. The variance is the average of the squared differences from the mean. Its symbol is σ (the greek letter sigma).

### Arithmetic Formula to Calculate Standard Deviation

To calculate the standard deviation, you need to calculate the variance first as the standard deviation is the square root of the variance. The standard deviation can be of 2 kinds. They are population standard deviation and sample standard deviation. The formula for calculating the standard deviation is given below.

**Population Standard Deviation**

**Sample Standard Deviation**

For both equations,

**μ**is the arithmetic mean**X**is the individual value**N**is the size of the population**σ**is the standard deviation

## Basic Examples to Calculate Mean and Standard Deviation in Excel

### Example 1 – Mean Deviation Calculation with Formula

** Steps**:

- Organize your dataset.

- Apply the following formula to count the number of values.

`=COUNT(D5:D7)`

The **COUNT function **counts the number of values in cell **D5:D7**.

- Enter the following formula to calculate the
**Mean**.

`=AVERAGE(D5:D7)`

The** AVERAGE function **calculates the mean in the range **D5:D7**.

- Calculate the
**Median**using the following formula:

`=MEDIAN(D5:D7)`

The **MEDIAN function **calculates the median in the range **D5:D7**.

- Calculate the absolute value of the difference between the share value and the mean value.

`=ABS(C15-$D$10)`

**C15 **= Share value

**D10 **= Mean Value

- Use
**Fill Handle**to**AutoFill**the rest of the cells.

- Calculate the absolute value of the difference between the share value and the median value.

`=ABS(C14-$D$11)`

**C14 **= Share value

**D11 **= Median Value

**AutoFill**the remaining cells.

- Calculate the
**Sum of the absolute value of (X-μ)**with the formula:

`=SUM(D14:D16)`

The **SUM function** adds the value in the cells **D14:D16**.

- Calculate the
**Sum of the absolute value of (X-M)**using the formula below:

`=SUM(E14:E16)`

The **SUM function** adds the value in the cells **E14:E16**.

- Apply the following formula to calculate
**Mean Deviation From Mean**:

`=D18/D9`

**D18 **= Sum of the absolute value of (X-μ)

**D9 **= Number of Share Values

- Apply the following formula to calculate the
**Mean Deviation**from the**Median**:

`=D19/D9`

**D19 **= Sum of the absolute value of (X-M)

**D9 **= Number of Share Values

### Example 2 – Standard Deviation Calculation with Formula

** Steps**:

- Organize your dataset.
- Apply the following formula to calculate
**Total number of data (N)**:

`=COUNT(D5:D9)`

The **COUNT function **returns the number of frequencies in cell **D5:D9**.

- Apply the following formula to calculate the
**Arithmetic Mean (μ)**:

`=AVERAGE(D5:D9)`

The** AVERAGE function **calculates the mean in the range **D5:D9**.

- Calculate the
**Deviation about the mean (X-μ)**with the formula below:

`=D5-$F$12`

**D5 **= frequency value

**F12 **= Arithmetic Mean

**AutoFill**the remaining cells.

- Calculate the
**Square of the deviation about the mean (X-μ)^2**with the formula below:

`=E5^2`

**AutoFill**the remaining cells.

- Find the
**Sum of the square of the deviation about the mean (X-μ)^2**with the formula:

`=SUM(F5:F9)`

The **SUM function **added the value in cells **F5:F9**.

- Measure
**Population variance (σ^2)**with the following formula:

`=F13/F11`

**F13 **= **Sum of the square of the deviation about the mean (X-μ)^2
F11** =

**Total number of data**

- Apply the following formula to calculate
**Standard Deviation from Population Variance**:

`=F14^0.5`

**F14 **defines **Population variance**.

- To find
**Sample Variance (σ^2)**, enter the following formula:

`=F13/(F11-1)`

**F13 **= **Sum of the square of the deviation about the mean (X-μ)^2
F11** =

**Total number of data**

- Enter the following formula to get the
**Standard Deviation from Sample Variance**:

`=F16^0.5`

**F16** represents** Sample Variance**.

**Read More: **How to Calculate Standard Deviation with IF Conditions in Excel

## Calculating Mean and Standard Deviation Using Built-in Excel Functions

### Method 1 – Mean Deviation From Mean

We can calculate the **Mean Deviation **From the** Mean **with the **AVEDEV function**.

The formula is:

`=AVEDEV(C5:C9)`

** **

### Method 2 – Population Standard Deviation

We can calculate the **Population Standard Deviation **with the **STDEV.P function**.

The formula is:

`=STDEV.P(C5:C9)`

### Method 3 – Sample Standard Deviation

We can calculate **Sample Standard Deviation **with the **STDEV.S function.**

The formula is:

`=STDEV.S(C5:C9)`

## Calculating Different Types of Standard Deviations in Excel

**Function 1 – STDEV.P Function**

To calculate **Standard deviations **with the **STDEV.P function**, use the following formula:

`=STDEV.P(D5:D9)`

**Function 2 – STDEVPA Function**

To calculate **Standard deviations **with the **STDEVPA function**, use the following formula:

`=STDEVPA(D5:D9)`

**Read More:** How to Calculate Standard Deviation of y Intercept in Excel

**Function 3 – STDEV.S Function**

To calculate **Standard deviations **with the **STDEV.S function, **use the following formula:

`=STDEV.S(D5:D9)`

**Function 4 – STDEVA Function**

Using the **STDEVA function** to calculate **Standard deviations **takes into account logical values too.

Use the following formula:

`=STDEVA(D5:D9)`

**Download Practice Workbook**

**Related Articles**

- How to Calculate Standard Deviation of a Frequency Distribution in Excel
- Calculate Percentile from Mean and Standard Deviation in Excel
- How to Calculate Uncertainty in Excel

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