About

In statistics, an "average" is not a single concept but a collection of measures of central tendency. Relying solely on the Arithmetic Mean can be misleading, especially in datasets containing outliers (e.g., salary data where one billionaire skews the results). Data analysts use different types of averages to accurately describe the typical value of a set.

This tool computes the four primary statistical descriptors simultaneously. It identifies the Mean (mathematical average), Median (the middle value), Mode (most frequent value), and Range (spread). It also calculates the Geometric Mean, which is critical for analyzing growth rates and financial returns where compounding is involved.

Formulas

Standard statistical definitions used in this engine:

Arithmetic Mean (x):

x = 1n n∑i=1 x_i

Geometric Mean (G):

G = &supn;x₁ x₂ ⋯ x_n

Harmonic Mean (H):

H = nn∑i=1 1x_i

Reference Data

Type	Formula Concept	Best Used For	Sensitivity to Outliers
Arithmetic Mean	Sum / Count	Normal distributions, daily temps.	High (Very Sensitive)
Median	Middle Value	Income, Home Prices, skewed data.	Low (Robust)
Mode	Most Frequent	Voting, product sales, categorical data.	N/A
Geometric Mean	N-th root of Product	Investment returns, bacteria growth.	Moderate
Harmonic Mean	N / Sum of Reciprocals	Speed, rates, density.	Sensitive to low values
Range	Max - Min	Measuring dispersion/spread.	High

Frequently Asked Questions

Use the Median when your data is skewed or contains extreme outliers. For example, if ten people earn $50k and one earns $10M, the Mean is misleadingly high (~$1M), but the Median accurately reflects the typical $50k salary.

Yes. A dataset can be bimodal (two modes) or multimodal. If all numbers appear only once, there is no mode. This tool will list all modes found.

It accounts for the compounding nature of returns. If an asset drops 50% one year and gains 50% the next, the Arithmetic Mean is 0%, but the Geometric Mean correctly shows a loss, as you have less money than you started with.

Yes, for Arithmetic Mean, Median, and Mode. However, Geometric and Harmonic means are generally undefined or complex for datasets containing negative numbers or zeros.