Variance - Formula, Steps to calculate variance, Example, Advantages and Disadvantages

The term variance indicates a statistical measurement of the difference between the given numbers in a data set. More clearly, variance is how far each number in the data set is from the mean and thus from the other numbers in the group. It is represented by the symbol σ2. The square root of the variance is standard deviation σ. Both analysts and many traders use the variance in determining the volatility and the market security.

How is it calculated?

Variance measures the variability of a number from either the mean or from the other number in the given data set. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and dividing the sum of the squares by the number of values in the data set.

When the data is collected from every member of the population and used in the data set, then we get the population variation and the exact values.

Population variance σ² = (X- μ)2N

σ² = population variance

Σ = sum of…

Χ = each value

μ = population mean

Ν = number of values in the population

Sample Variance is used to make estimates about the population variance. It is calculated by using the following formula:

Sample variance σ² =​ i=1n(xi - x)2n-1

where:

x_i = i^th data point

x = Mean of all data points

n = Number of data points

A small variance indicates that numbers in the set are near the mean and near each other. A significant variance, on the other hand, indicates the opposite. A zero variance value indicates that all values within a set of numbers are identical. A variance cannot be negative. Every variance that is not zero is a positive number. It is mathematically impossible since we cannot have a negative value resulting from a square.

Steps to calculate variance

• Find the mean
• Find each score’s deviation from the mean
• Square each deviation from the mean
• Find the sum of squares
• Divide the sum of squares by n-1 or N

Advantages

• How the number relates each other
• Faster than those broad mathematical techniques of arranging numbers in quartilesv
• All deviations are treated same
• Treated same regardless of the direction
• Squared deviations cannot sum to zero
• They give the appearance of no variability at all in the given data set

Disadvantages

• Gives added weight to the outliers (numbers far from the mean)
• Squaring those numbers can skew the data
• Not easily interpreted
• Users get confuse between variance and standard deviation and does mistakes readily

Example

Let’s calculate the variance of the following data set: 2, 7, 3, 12, 9. The first step is to calculate the mean. The sum is 33 and there are 5 data points. Therefore, the mean is 33 ÷ 5 = 6.6. Then you take each value in the data set, subtract the mean and square the difference. For instance, for the first value: (2 - 6.6)2 = 21.16 The squared differences for all values are added: 21.16 + 0.16 + 12.96 + 29.16 + 5.76 = 69.20 The sum is then divided by the number of data points: 69.20 ÷5 = 13.84 The variance is 13.84. To get the standard deviation, you calculate the square root of the variance, which is 3.72.