Variance is a commonly used statistical measure to understand the spread or dispersion of a set of data. It is especially useful in the fields of finance, economics, and research. In this comprehensive guide, we will walk you through the step-by-step process of calculating variance.

What is Variance?

Variance measures how far each number in a dataset is from the mean and hence provides insights into the variability of the data. A high variance indicates a greater range of values, while a low variance indicates a more concentrated cluster of values.

How to Calculate Variance:

To calculate the variance, you need to follow these steps:

  • Step 1: Determine the mean of the data set
  • Step 2: Subtract the mean from each data point
  • Step 3: Square the result of each subtraction
  • Step 4: Sum all the squared values
  • Step 5: Divide the sum by the total number of data points (N)

Let’s explore each step in more detail:

Step 1: Determine the mean of the data set

To calculate the mean, sum up all the numbers in the data set and divide by the total number of data points. Let’s say we have a data set with the following numbers:

Example:

  • 5
  • 10
  • 15
  • 20
  • 25

The sum of these numbers is 5 + 10 + 15 + 20 + 25 = 75. Since there are 5 data points, the mean will be 75 / 5 = 15.

Step 2: Subtract the mean from each data point

Now, subtract the mean from each of the data points in the set. Continuing from our example:

  • 5 – 15 = -10
  • 10 – 15 = -5
  • 15 – 15 = 0
  • 20 – 15 = 5
  • 25 – 15 = 10

Step 3: Square the result of each subtraction

Square each result obtained from the previous step. Squaring ensures that the values are positive and gives more weight to larger deviations from the mean.

  • (-10)^2 = 100
  • (-5)^2 = 25
  • (0)^2 = 0
  • (5)^2 = 25
  • (10)^2 = 100

Step 4: Sum all the squared values

Add up all the squared values obtained in the previous step to calculate the sum of squared deviations:

100 + 25 + 0 + 25 + 100 = 250

Step 5: Divide the sum by the total number of data points (N)

Finally, divide the sum of squared deviations by the total number of data points (N) to obtain the variance:

Variance = 250 / 5 = 50

So, in our example, the variance of the data set is 50.

Calculating variance is an essential statistical technique that provides valuable insights about the variability of a dataset. By following the step-by-step process outlined in this guide, you can effortlessly calculate the variance of any dataset. Remember, understanding variance is crucial in many fields, including finance, economics, and research.

Now that you know how to calculate variance, you can apply this knowledge to analyze and interpret data effectively.

Quest'articolo è stato scritto a titolo esclusivamente informativo e di divulgazione. Per esso non è possibile garantire che sia esente da errori o inesattezze, per cui l’amministratore di questo Sito non assume alcuna responsabilità come indicato nelle note legali pubblicate in Termini e Condizioni
Quanto è stato utile questo articolo?
0Vota per primo questo articolo!