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# What Is Variance In Statistics? Definition, Formula, And Example

Published: February 15, 2024

Learn the definition, formula, and example of variance in statistics in this comprehensive guide. Enhance your finance knowledge now!

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## What Is Variance in Statistics? Definition, Formula, and Example

Welcome to our “FINANCE” blog category where we delve into various aspects of the finance world. In today’s post, we are going to explore an important statistical concept – variance. Whether you’re a finance professional, a student studying statistics, or simply curious about the topic, this article will provide you with a comprehensive understanding of variance, including its definition, formula, and examples. So, let’s dive right in!

## Key Takeaways:

- Variance is a measure of how spread out a set of data points is.
- It quantifies the variability or dispersion between individual data points relative to the mean.

## Definition

Variance is a statistical measurement that quantifies the dispersion between individual data points and the mean of a dataset. It provides a measure of how spread out the data values are. In other words, variance tells us how much the data points deviate from the average or expected value.

## Formula

The formula for calculating variance depends on whether you are dealing with a population or a sample. Let’s take a look at both:

**Population Variance:**

The population variance is represented by σ² (sigma squared) and is calculated using the following formula:

**σ² = (Σ(x – μ)²) / N**

- σ²: Population variance
- Σ: The sum of (x – μ)² for all data points in the population
- μ: Population mean
- N: Number of data points in the population

**Sample Variance:**

The sample variance is denoted as s² (squared) and is calculated using the following formula:

**s² = (Σ(x – x̄)²) / (n – 1)**

- s²: Sample variance
- Σ: The sum of (x – x̄)² for all data points in the sample
- x̄: Sample mean
- n: Number of data points in the sample

## Example

Let’s illustrate the concept of variance with a simple example. Consider a finance analyst who wants to measure the variability in daily stock returns of a particular company over the past month. The analyst collects the following daily returns data:

- Day 1: 1.5%
- Day 2: -2.2%
- Day 3: 0.8%
- Day 4: 3.1%
- Day 5: -1.7%

To calculate the variance, we first need to find the mean of these daily returns. The mean is obtained by summing up all the values and dividing by the total number of data points:

Mean = (1.5% – 2.2% + 0.8% + 3.1% – 1.7%) / 5 = 0.5%

Next, we calculate the sum of squared differences from the mean for each data point:

- (1.5% – 0.5%)² = 1%
- (-2.2% – 0.5%)² = 7.29%
- (0.8% – 0.5%)² = 0.09%
- (3.1% – 0.5%)² = 7.84%
- (-1.7% – 0.5%)² = 4.84%

Finally, we calculate the variance by summing up these squared differences and dividing by the total number of data points:

Variance = (1% + 7.29% + 0.09% + 7.84% + 4.84%) / 5 = 4.61%

In this example, the calculated variance is 4.61%, indicating the degree of dispersion or variability in the daily stock returns over the past month.

## Conclusion

Variance is a crucial statistical concept in finance and other fields. By quantifying the dispersion of data points relative to the mean, variance provides valuable insights into the variability of a dataset. Whether you’re analyzing stock returns, market trends, or any other financial data, understanding variance is essential for making informed decisions.

We hope this article has given you a clear understanding of variance, its definition, formula, and how it can be applied. Keep exploring our “FINANCE” category for more informative articles that can help you navigate the world of finance!