Variance: What it is and how it is calculated

The Variance is, along with the standard deviation, the most commonly used measure of dispersion. It is a reliable measure for analyzing data from a distribution. By comparing to the mean, the presence of outliers or deviating data can be identified.

Below you will learn more about this measure, its properties, benefits and how it is calculated.

What is the variance?

Variance is a measure of spread that represents the variability of a data series relative to its mean. Formally, it is calculated as the sum of the squares of the residuals divided by the total number of observations.

It can also be calculated as the standard deviation squared. By the way, the residual is the difference between the value of a single variable and the mean of the entire variable.

Calculating the variance is necessary to calculate the standard deviation.

  | You might be interested to know what it is Mean, the median and the mode are.

Advantages and disadvantages of variance

Variance is used to see how individual numbers within a data set are related, rather than using broader mathematical techniques.

It also differs in that it treats all deviations from the mean as equal, regardless of their direction. The squared deviations cannot add up to zero and give the appearance that there is no variability in the data.

One disadvantage, however, is that more weight is given to outliers. These are numbers that are far from the mean. Squaring these numbers can distort the data.

Another disadvantage of variance is that it is not easy to interpret. It is mainly used to take the square root of its value, which indicates the standard deviation of the data.

Example of the variance

A hypothetical example will be used to illustrate how variance works, in this case in the area of ​​finance. Suppose the return on shares of Company ABC is 10% in the first year, 20% in the second year, and -15% in the third year. The average of these three returns is 5%. The differences between individual returns and the mean are 5%, 15% and -20% for each consecutive year.

Squaring these deviations gives 0,25%, 2,25% and 4,00%, respectively. If we square these deviations, we get a total of 6,5%. If you divide the sum of 6,5% by 1 minus the number of returns in the data set since it is a sample (2 = 3-1), you get a variance of 3,25% (0,0325). The square root of the variance gives a standard deviation of returns of 18% (√0,0325 = 0,180).

How to calculate the variance

To calculate the variance, follow these steps:

• Calculate the mean of the data.
• Determine the difference between the individual data points and the mean.
• Square each of these values.
• Add all squared values.
• Divide this sum of squares by n – 1 (for a sample) or N (for the population).

Formula for calculating variance

Before we look at the formula, it must be said that variance is very important in statistics. Although it is a simple measure, it can provide a lot of information about a particular variable.

The unit of measurement is always the unit of measurement that corresponds to the data, but squared. The variance is always greater than or equal to zero. Since the residuals are squared, it is mathematically impossible for the variance to be negative. Therefore it cannot be smaller than zero.

What is the difference between variance and standard deviation?

Actually, they both measure the same thing. The variance is the standard deviation squared. Conversely, the standard deviation is the square root of the variance.

The standard deviation is calculated in the original units of measurement. Since this is normal, one might naturally ask what the point of variance as a concept is. Well, although the interpretation of the value it provides does not give us much information, its calculation is necessary to obtain the value of the other parameters.

To calculate covariance we need the variance and not the standard deviation, to calculate some econometric matrices we use the variance and not the standard deviation. This is a matter of convenience when working with the data and depends on the specific calculations.

   |  Also find out more about the mean deviation.

Why is standard deviation often used more than variance?

The standard deviation is the square root of the variance. It is sometimes more useful because the square root removes the units from the analysis. This allows direct comparisons to be made between different things, which may have different units or different sizes.

For example, by saying that increasing X by one unit increases Y by two standard deviations, one can understand the relationship between X and Y regardless of the units in which they are expressed.

Conclusion

The variance is used in statistics and probability as a measure of the spread of a distribution or sample. More precisely, it is defined as the mean of the squares of the deviations from the mean. Taking the square of these deviations into account prevents the positive and negative deviations from canceling each other out.

Visually, a distribution with a large variance is more widely dispersed, while a distribution with a small variance is very closely spaced around its mean.

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KEYWORDS OF THIS BLOG POST

Variance | standard deviation | Market research