**What is Variance?**

Variance is a statistical measure that indicates **the spread** or dispersion of a set of data points.

In simpler terms, it tells us **how far each number in a dataset is from the mean** and thus, gives an idea of the distribution of data points. The formula to calculate variance (for a sample) is:

- is the sample variance
- is each individual data point
- is the mean of the data
- is the number of data points

**How to Calculate Variance**

Let’s calculate the variance for the dataset: 2, 4, 4, 4, 5, 5, 7, 9.

**Step 1: Calculate the Mean**

First, we need to find **the mean **(average) of the dataset.

Here we get the mean, 5.

**Step 2: Subtract the Mean and Square the Result**

Next, subtract the mean from each data point and square the result.

**Step 3: Calculate the Average of the Squared Differences**

Now, find the average of those squared differences.

So, the variance of the dataset is **4**.

**Variance vs Standard Deviation**

Both variance and **standard deviation** provide insights into the dispersion of a dataset.

However, while variance gives the average of the squared differences from the Mean, **the standard deviation is the square root of the variance**.

This makes standard deviation more interpretable as it’s in the same unit as the data, whereas variance is in squared units.

**Using the previous dataset(2, 4, 4, 4, 5, 5, 7, 9)**, if the variance is **4** (squared units),** the standard deviation** would be the square root of that, approximately **2**, which is in the original unit of the data.

**Sample Variance vs Population Variance**

**1. Sample Variance**

Calculated when dealing with a **sample** of a population.

It uses in the denominator to provide **an unbiased estimate** for the population variance.

*Formula:*

Remember, is **the mean(average) of sample.**

**2. Population Variance**

Calculated when dealing with **an entire population**. It uses in the denominator.

*Formula:*

is **the population mean** and is the total number of data points in the population.

Remember, practice makes perfect. Try calculating variance with different datasets to get a better grasp of the process.

**Usages of Variance in Business**

**Usage in Finance**

Variance is used in portfolio theory to determine **the volatility of assets**.

A higher variance indicates a more volatile asset, which might be riskier but could also offer higher returns.

**Usage in Marketing**

In A/B testing, variance helps in understanding **the consistency in the behavior of two different test groups**.

A high variance might indicate that an observed behavior isn’t consistent and might not be a true representation of the entire population.

**Usage in Supply Chain Management**

Variance in demand or supply can indicate **potential disruptions**.

By monitoring variance, businesses can adjust their strategies to ensure smooth operations.