**Variance Analysis Formula (Table of Contents)**

## What is the Variance Analysis Formula?

Variance analysis is a quite important formula used in portfolio management and other financial and business analysis. The quantitative formula can be measured as the difference between planned and actual numbers. The formula is heavily used in cost analysis to check the variance between the planned or the standard cost versus the actual cost. The analysis helps the management to keep a check on the operational performance of the company.

Formula For Variance Analysis is given below

**Variance = (X – µ)**

^{2 }/ N**X**stands for the value of individual data point**µ**stands for the average or the mean of the individual data point**N**stands for the number of individual data points in a given array

Variance analysis formula is used in a probability distribution set up and variance as also be defined as the measure of risk from an average mean. Variance also depicts how much the investor is able to assume the risk when purchasing a specific security.

**Examples of Variance Analysis Formula (With Excel Template)**

Let’s take an example to understand the calculation of the Variance Analysis in a better manner.

#### Variance Analysis Formula – Example #1

**Consider a data set having the following observations 2,3,6,6,7,2,1,2,8. We need to calculate the variance analysis.**

The solution to the following problem can be solved by taking the following steps:

Mean is calculated as:

Now, we need to calculate the difference between the data points and the mean value.

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Similarly, calculate for all values of the data set.

Calculate the square of the difference between data points and the mean value.

Variance Analysis is calculated using the formula given below

**Variance = (X – µ) ^{2 }/ N**

In the first step, we have calculated the mean by summing (2+3+6+6+7+2+1+2+8)/number of observation which gives us a mean of 4.1. Then in column 2, we have calculated the difference between the data points and the mean value and squaring each value individually. After that summing up of column C and dividing it by the number of observation gives us the variance of 5.8.

#### Variance Analysis Formula – Example #2

**The heights of the dogs in a given set of a random variable are 300 mm, 250 mm, 400 mm, 125 mm, 430 mm, 312 mm, 256 mm, 434 mm and 132 mm. Calculate the variance analysis of the data set from the mean.**

The solution to the following problem can be solved by taking the following steps:

Mean is calculated as:

Now, we need to calculate the difference between the data points and the mean value.

Similarly, calculate for all values of the data set.

Calculate the square of the difference between data points and the mean value.

Variance Analysis is calculated using the formula given below

**Variance = (X – µ) ^{2 }/ N**

In the first step, we have calculated the mean by summing (300+250+400+125+430+312+256+434+132)/number of observation which gives us a mean of 293.2. Then in column 2, we have calculated the difference between the data points and the mean value and squaring each value individually. After that summing up of column C and dividing it by the number of observation gives us the variance of 11985.7.

#### Variance Analysis Formula – Example #3

**The marks gained by the students selected from a large sample of 100 students are 12, 15, 18,24,36, 10. Calculate the variance analysis of the data from the mean.**

The solution to the following problem can be solved by taking the following steps:

Mean is calculated as:

Now, we need to calculate the difference between the data points and the mean value.

Similarly, calculate for all values of the the data set.

Calculate the square of the difference of data points and the mean value.

Variance Analysis is calculated using the formula given below

**Variance = (X – µ) ^{2 }/ N**

In the first step, we have calculated the mean by summing (12+15+18+24+36+10)/number of observation which gives us a mean of 19.2. Then in column 2, we have calculated the difference between the data points and the mean value and squaring each value individually. After that summing up of column C and dividing it by the number of observation gives us the variance of 76.8

### Explanation

The variance analysis formula is calculated using the following steps:-

**Step 1:** Calculate the mean of the number of observations present in the data array which can we calculated by a simple mean formula which is the sum of all the observations divided by the number of observations.

**Step 2:** After calculating the mean of the observations each observation is subtracted from the mean in order to calculate the deviation of each and every observation from the mean.

**Step 3:** The difference of each observation is then summed and is squared to avoid the negative-positive signage and is then divided by the number of observations.

### Relevance and Uses of Variance Analysis Formula

The variance analysis can be used in the following areas:-

- Portfolio Management
- Calculation of stock and portfolio return
- Budget VS Actual Cost comparison which is used very frequently in the business
- Forecasting of cost and revenue
- Materiality
- Relationships between two variables

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