Average Calculator

Calculate mean, median, mode, and range of a set of numbers.

Enter numbers (comma or space separated)

Mean (Average)

Median

Mode

Sum

Count

Range

Min

Max

Std Dev

How It Works

Enter a list of numbers separated by commas or on separate lines. The calculator computes the mean, median, mode, range, variance, and standard deviation.

**Average Calculator — Descriptive Statistics Made Easy**

Statistics is the language of data, and descriptive statistics — the basics of summarising a dataset — are used everywhere from science to business to everyday decision-making. Our Average Calculator computes all key measures of central tendency and spread.

**Measures of Central Tendency**

**Mean (Arithmetic Average)**
Sum of all values ÷ Count of values
Example: {3, 7, 5, 9, 6} → Mean = 30/5 = 6.0
Best for: Symmetric distributions without outliers

**Median (Middle Value)**
The middle value when data is sorted
Example: {3, 5, 6, 7, 9} → Median = 6
Best for: Skewed data or when outliers are present (e.g., income data)

**Mode (Most Frequent Value)**
The value that appears most often
Example: {3, 5, 5, 7, 9} → Mode = 5
Best for: Categorical data and finding the most common value

**Measures of Spread**

**Range**
Range = Maximum – Minimum
Example: {3, 5, 6, 7, 9} → Range = 9 – 3 = 6

**Variance**
Average of squared deviations from the mean

**Standard Deviation**
Square root of variance; measures typical distance from the mean

**Practical Applications**

*Academic grades* — Calculate class average, identify median grade, spot modes.
*Financial data* — Average stock returns, median income, price volatility (standard deviation).
*Scientific experiments* — Describe experimental results, assess variability.
*Quality control* — Manufacturing tolerances (Six Sigma uses ±6 standard deviations).

**When Mean ≠ Median (Skewed Data)**

For house prices in a city, the median is more informative than the mean. A single billionaire in a neighbourhood skews the mean household income dramatically while the median remains representative. This is why income statistics typically report median household income.

Frequently Asked Questions

Mean is the sum divided by count. Median is the middle value when sorted. For skewed data (like incomes), median is more representative because it's resistant to extreme outliers.

If all values appear exactly once, there is no mode. If multiple values appear equally often, all are modes (multimodal distribution).

Standard deviation measures how spread out values are from the mean. A small SD means values cluster near the mean; a large SD means they spread widely.

There is no practical limit. Enter as many numbers as needed, separated by commas, spaces, or line breaks.

Population SD (σ) divides by N; sample SD (s) divides by N-1 (Bessel's correction). Use sample SD when your dataset is a sample from a larger population.