---
title: "How to Calculate Mean, Median, Mode, and Standard Deviation"
description: "Step-by-step guide to statistics basics. Learn mean (average), median, mode, range, variance, and standard deviation with real number examples. When to use each measure — explained simply."
url: "https://worldcalculators.org/learning/how-to/mean-median-mode-std-dev/"
canonical: "https://worldcalculators.org/learning/how-to/mean-median-mode-std-dev/"
---

# Mean, Median, Mode & Standard Deviation

Step-by-step guide to statistics basics. Learn mean (average), median, mode, range, variance, and standard deviation with real number examples. When to use each measure — explained simply.

## Quick answer

For the dataset [3, 7, 7, 9, 12] : Mean = (3+7+7+9+12)/5 = 7.6 . Median = middle value = 7 . Mode = most frequent = 7 . Range = 12−3 = 9 . Standard deviation ≈ 2.94 (measures spread). Use median for skewed data like salaries; mean for symmetric data like test scores.

## Mean (Average)

Formula: Mean = Sum of all values ÷ Count of values
Example: test scores [72, 85, 91, 68, 94]

## Median (Middle Value)

Odd count: Sort values, pick the middle one. Even count: Sort, average the two middle values.
Example: salaries [$30k, $200k, $35k, $40k, $45k]

## Mode (Most Frequent Value)

The mode is the value that appears most often. There can be no mode, one mode, or multiple modes.

## Standard Deviation (Spread)

Standard deviation measures how spread out values are from the mean. Small SD = values clustered near the mean. Large SD = values spread wide.
Sample SD: divide by (n − 1) in step 3, not n. Use sample SD when your data is a sample from a larger population (which is almost always).

Source: https://worldcalculators.org/learning/how-to/mean-median-mode-std-dev/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.