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What is Variance? How to Calculate it?

Published by at September 2nd, 2021 , Revised On October 5, 2021

If the term variance has bothered you like many of the students out there, you have made it to the right place. This blog covers everything you need to know about variance, from the definition to its calculation.

First things first, let’s discuss what variance is before getting into some daunting calculations.

Definition of Variance

A statistical measurement of the dispersion between values in a data collection is known as a variance. Variance expresses how far each number in the set deviates from the mean and thus from every other number in the set. The symbol that is frequently used to represent variation is σ2. Analysts and traders use it to gauge market volatility and security. The standard deviation (σ) is the square root of the variation, which helps determine the consistency of an investment’s returns over time.

Having said that, let’s now try to understand how standard deviation is related to variance.

Standard Deviation and Variance 

For those of you who often confuse variance with standard deviation, here is what you need to know.

The standard deviation is generated from variance and indicates how far each number deviates from the mean on average. The square root of the variance is what it is. Both metrics indicate distribution variability, although their units are different. The original values are expressed in the same units as the standard deviation (e.g., meters). Variance is measured in far bigger units than standard deviation (e.g., meters squared).

The variance number is more difficult to grasp intuitively since the units of variance are substantially larger than the units of a typical value in a data collection. As a result, the standard deviation is frequently used as a primary measure of variability.

The variance, rather than the standard deviation, provides more information on variability and is used to make statistical inferences.

Standard deviation is more sensitive than the semi-quartile range, yet being less susceptible to high values than the range. The semi-quartile range should complement the standard deviation if the chance of high values (outliers) exists.

Formula of Variance

As the name itself says, we have already mentioned that variance calculates variability from the mean or average. It is measured by taking the differences between each number and then the mean. Next is squaring the differences to make positive and then dividing the square sum by the total number of values in the data set.

Don’t worry, the formula is not as complicated as it sounds.

The formula for calculating the variance is:

Variance σ2=n−1∑i=1n​(xi​−xˉ) 2​

Here,

xi is the ith data point

xˉ is the mean of all data points

and n is the number of data points​

A high variance indicates that the numbers in the set are both far from the mean and far apart from each other. On the other hand, a small variation indicates the polar opposite. However, a variance of zero indicates that all values within a set of numbers are the same. Every non-zero variance is a positive number. It is impossible for a variance to be negative. This is due to the fact that it is mathematically impossible.

Now that we are done with the formula let us look at some of the advantages and disadvantages of variance.

Disadvantages and Advantages of Variance 

Rather than utilizing broader mathematical strategies like g

grouping numbers into quartiles, statisticians utilize variance to see how individual numbers within a data set relate to one another. The benefit of variance is that it treats all departures from the mean equally, regardless of direction. The squared deviations cannot equal 0, giving the impression that there is no variability in the data.

However, one disadvantage of variance is that it gives outliers more weight. These are the numbers that are out of the ordinary. Squaring these numbers can cause the data to become skewed. Another disadvantage of utilizing variance is that it is difficult to interpret. The square root of its value, which reflects the data set’s standard deviation, is one of the most common uses for it. Standard deviation can be used by investors to determine how consistent returns are throughout time, as previously mentioned.

That is all for this guide, if you have any queries or questions, please leave a comment in the comments section below.

FAQs About Variance

A statistical measurement of the dispersion between values in a data collection is known as a variance. Variance expresses how far each number in the set deviates from the mean, and thus from every other number in the set. The symbol is frequently used to represent variation is σ2.

The variance number is more difficult to grasp intuitively since the units of variance are substantially larger than the units of a typical value in a data collection. As a result, the standard deviation is frequently used as a primary measure of variability.
The variance, rather than the standard deviation, provides more information on variability and is used to make statistical inferences.
Standard deviation is more sensitive than the semi-quartile range, yet being less susceptible to high values than the range. The semi-quartile range should complement the standard deviation if the chance of high values (outliers) exists.

The formula for calculating the variance is:

Variance σ2=n−1∑i=1n(xi−xˉ) 2

Here,

xi is the ith data point

xˉ is the mean of all data points

and n is the number of data points

The benefit of variance is that it treats all departures from the mean equally, regardless of direction. The squared deviations cannot equal 0, giving the impression that there is no variability in the data. However, one disadvantage of variance is that it gives outliers more weight. These are the numbers that are out of the ordinary. Squaring these numbers can cause the data to become skewed.

About Owen Ingram

Ingram is a dissertation specialist. He has a master's degree in data sciences. His research work aims to compare the various types of research methods used among academicians and researchers.