Statistics Calculator

This is a simple, general-purpose statistics calculator that computes key statistical measures, including the mean, population Standard Deviation  (σ), sample standard deviation (s), and geometric mean, among others.

Many of these metrics are explained in greater detail in other specialized calculators available on this website. Follow the provided hyperlinks to learn more about their calculations, see basic examples, and explore practical applications.

Note on Variance: Although variance is not displayed directly, it is derived by squaring the standard deviation (σ² or s²). Simply ensure you’re using the correct standard deviation (population σ or sample s) and square the value to obtain the variance.

What Is the Geometric Mean?

The geometric mean is a type of average that measures central tendency by using the product of a set of values, rather than their sum (as in the arithmetic mean). It is particularly useful when dealing with data that spans vastly different scales or ranges.

Why Use the Geometric Mean Instead of the Arithmetic Mean?

Consider a car rated on two different scales:

• Fuel efficiency: Scored from 0 to 5

• Safety: Scored from 0 to 100

If we used the arithmetic mean, the safety score (on a much larger scale) would disproportionately influence the result. For example:

• A jump in fuel efficiency from 2 to 5 (a 150% increase) would be dwarfed by a safety score change from 80 to 85 (just a 6.25% increase).

The geometric mean corrects this imbalance by normalizing the scales, ensuring no single variable dominates the average. Unlike the arithmetic mean, a percentage change in any value affects the geometric mean equally, making it ideal for comparing ratios or widely varying ranges.

In the equation above, i is the index that refers to the location of a value in a set, x_i is an individual value, and N is the total number of values. i=1 refers to the starting index, i.e. for a data set 1, 5, 7, 9, 12, i=1 is 1, i=2 is 5, i=3 is 7, and so on. The notation above essentially means to multiply each value in the set through the n^th value, and then take the n^th root of the product. Refer to the Root Calculator if necessary for a review of n^th roots. Below is an example using the listed data set:

The geometric mean has applications within proportional growth, the social sciences, aspect ratios, geometry, and finance among others, and like most other statistical values, can provide highly useful information when used in the proper contexts.

Related Calculators:
Probability Calculator , Binary Calculator

External Resources:
Statistics Calculator on Calculator.net