Variance Calculator

Understanding Variance

Variance is a statistical measurement that describes the spread of numbers in a dataset. It indicates how much the numbers in a set differ from the mean (average) of that set. A high variance means that the numbers are more spread out, while a low variance indicates that they are closer to the mean.

Interesting Facts About Variance

• Variance is used in various fields, including finance, science, and engineering, to assess risk and variability.
• The square root of variance is known as the standard deviation, which is often used to understand the dispersion of data.
• In finance, variance is a key component in portfolio theory, helping investors understand the risk associated with different investment options.

How to Calculate Variance

To calculate variance, follow these steps:

1. Find the mean of the dataset.
2. Subtract the mean from each number to find the deviation of each number.
3. Square each deviation.
4. Find the average of these squared deviations.

Variance Formula

$$\sigma^2 = \frac{\sum_{i=1}^{N} (x_i – \mu)^2}{N}$$

Example for 5, 7, 3, 10, 4:

$$\sigma^2 = \frac{(5 – 5.8)^2 + (7 – 5.8)^2 + (3 – 5.8)^2 + (10 – 5.8)^2 + (4 – 5.8)^2}{5}$$
$$\sigma^2 = \frac{(-0.8)^2 + (1.2)^2 + (-2.8)^2 + (4.2)^2 + (-1.8)^2}{5}$$
$$\sigma^2 = \frac{0.64 + 1.44 + 7.84 + 17.64 + 3.24}{5}$$
$$\sigma^2 = \frac{30.8}{5} = 6.16$$

In this example, the mean is 5. The squared deviations are summed up to get 32, and then divided by the number of data points (8) to find the variance, which is 4.

Using the Variance Calculator

Input your data points into the Variance Calculator to quickly find the variance without manual calculations. This tool is beneficial for students, researchers, and professionals who need to analyze data efficiently.