Population Variance Calculator

Population variance is a specific measurement that’s expected on a given population. Should the measurement vary widely from individual to individual, you would expect a high variance. Conversely, if the measurement varies by just a small amount, then you would expect a small variance. To simplify the calculation of a population variance for a set of numbers, you can use this online population variance calculator.

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How to use the population variance calculator?

If you’re wondering how to find population variance, the simplest way to do this is by using a population variance calculator. With this simple online tool, you can acquire the value automatically without having to use a population variance formula to calculate manually. Here are the steps to follow when using this calculator:

  • All you have to do is enter the Numbers. In the space provided, enter two or more numbers and separate them using commas.
  • After that, the variance calculator will automatically give you the results which are the Total Numbers, Population Mean, and the Population Variance.


What is a population variance? 

Population variance is often used by statisticians whenever they deal with population data. You can easily calculate this value using this population variance calculator. You use this value in estimating how much the values of a population disperse or spread around a mean value. Here are some interpretations of the results you may get:

  • A zero population variance indicates that the observations for a specific population are the same.
  • A population variance that is less indicates that the data accumulates around the average value.
  • A population variance that is more indicates that the data is widely spread from the average.

Here are some points to consider when thinking about population variance:

  • Given that population variance is a measure for spread, the value for a group of the same points should be equal to zero.
  • The population variance will remain unchanged when adding a constant to each data point. For instance, if you make a study on the years of birth of all the senior citizens in Texas and decided to change calendars from the traditional one to one where you will consider 1900 as year 1. In this case, the population variance remains constant or unchanged.
  • The population standard deviation refers to the square root of the population variance.
  • Population variance is a function of the population. It’s never dependent on sampling practices or research methods.

Using a sample variance is highly recommended when making calculations on population variance becomes too tedious. The slight difference is that the sample variance uses a sample mean and the deviations get added up over this. Then you divide the sum by (n – 1). If you’re solving for the sample variance, n refers to how many sample points.

Not like the population variance which takes into account the population, the sample variance refers to the statistics of a certain sample. The sample variance will depend upon the sample you have chosen and research methodology.

Most likely, if you use a different sample or conduct a different experiment, this will yield a sample variance with a different value. However, if you have representative samples, then the resulting sample variance should yield adequate population variance estimates.


How do you calculate the variance of a population? 

How do you calculate the variance of a population 

Population variance or σ2 will indicate how data points for a particular population get spread out. The variance is the average distance of every data point in the population to the mean raised to the second power. Population variance is generally represented as  σ2, and you can calculate it using the following population variance formula:

σ2 = (1 /N) ∑ (xi – μ) 2



σ2 refers to the population variance

x1, …, xN refers to the population data set

μ refers to the mean of the population data set

N refers to the size of the population data set


Here are some steps to follow on how to find population variance without using a variance calculator:

  • First, compute the mean of the given data (μ). To do this, add all the observations then dividing the sum by how many observations.
  • Next, build a table and writing each mean value in the first column.
  • The second column will contain the deviation of every observation, and you calculate them using the mean. That is, you subtract the value of the mean from all of the given observations. This is mathematically represented by xi – μ.
  • In the third column, solve for the square of the deviation with this formula: (xi−μ)2
  • Compute for the sum of all the squared deviations using this part of the formula: ∑ni=1(xi−μ)2
  • Finally, divide the sum of the squared deviations by the number of total observations.


How do you calculate percentage variance? 

The percentage variance refers to a change in an account from one period to another, and you express it as a ratio. The change over that certain period can either be a decrease or increase in the account, and you show this as a percentage account value.

Percentage variances are essential in all kinds of decision making and financial planning because they aid investors, management, and creditors to keep track of the performance trends of companies.

It also helps in the evaluation of performance. Management specifically uses this in reviewing actual and budgeted numbers. With this, they can visualize how close the company is in relation to reaching their budgeted goals.

Creditors and investors, on the other hand, use the percentage variance model for financial analysis in tracking performance year after year. Use this formula to calculate percentage variance:

PV = (Current Year Amount – Prior Year Amount) / Prior Year Amount


When a company’s management uses this for their budget analysis, the formula changes slightly and becomes:

PV = (Budget Amount – Actual Amount) / Actual Amount


You can use these simple formulas to calculate items like variance between the current year and last year or for management or the variance between the budgeted and actual values. As the formulas illustrate, to calculate for a variance, you will need a baseline or a new value. If you can provide this, calculate the difference between the two values then divide by the original value.