Average Calculator – Find the Mean of Any Numbers

Calculate the average or arithmetic mean of any set of numbers with our free online mean calculator. Enter your values and get instant results – great for students, teachers, and analysts.

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Paste numbers from a spreadsheet, type them separated by commas, or enter each on a new line. The calculator handles any format.

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Average Calculator – Mean, Median, Mode & Statistics

The average – technically called the arithmetic mean – is the most common way to summarize a set of numbers. Add them all up and divide by how many you have. It's how teachers calculate grades, how analysts track performance, and how you figure out your monthly spending.

But the mean tells only part of the story. This calculator also gives you the median (middle value), mode (most frequent value), range, variance, and standard deviation. Together, these statistics paint a complete picture of your data's center, spread, and distribution.

Measures of Central Tendency

Mean (Average)

The sum of all values divided by the count. Most commonly used average, but sensitive to outliers.

Mean = Sum of values / Number of values

Example: (10 + 20 + 30) / 3 = 20

Median

The middle value when sorted. Half the values are above, half below. Resistant to outliers.

Sort values, find center

Example: 5, 8, 12, 15, 20 → Median = 12

Mode

The most frequently occurring value. A dataset can have one mode, multiple modes, or no mode.

Find most frequent value

Example: 3, 5, 7, 5, 7, 9 → Modes = 5, 7

Additional Statistics

Range

The difference between maximum and minimum values. Shows the spread of your data.

Range = Max - Min

Example: 5, 12, 18, 25 → Range = 25 - 5 = 20

Variance (σ²)

Average squared deviation from the mean. Measures how spread out the data is.

σ² = Σ(x - μ)² / N

Higher variance = more spread out data

Standard Deviation (σ)

Square root of variance. Shows typical distance from the mean in original units.

σ = √variance

68% of normal data falls within ±1σ of mean

Sum & Count

Basic totals. Sum is all values added together. Count is how many values you have.

Sum = x₁ + x₂ + ... + xₙ

Used to calculate the mean

Worked Examples

Example 1: Calculate Average Test Score

A student scored 85, 92, 78, 90, and 88 on five tests. What's their average?

Values: 85, 92, 78, 90, 88

Sum: 85 + 92 + 78 + 90 + 88 = 433

Count: 5

Mean: 433 / 5 = 86.6

Sorted: 78, 85, 88, 90, 92 → Median = 88

No repeated values → No mode

Example 2: Find Median with Even Count

Find the median of: 12, 5, 18, 9, 25, 3

Sorted: 3, 5, 9, 12, 18, 25

Count is even (6 values), so average the two middle values

Middle values: 9 and 12

Median: (9 + 12) / 2 = 10.5

Example 3: Calculate Standard Deviation

Find the standard deviation of: 4, 7, 13, 16

Mean: (4 + 7 + 13 + 16) / 4 = 10

Deviations from mean: -6, -3, 3, 6

Squared deviations: 36, 9, 9, 36

Variance: (36 + 9 + 9 + 36) / 4 = 22.5

Std Dev: √22.5 ≈ 4.74

Example 4: Mode in Real Data

A shoe store sold these sizes today: 8, 9, 7, 9, 10, 9, 8, 11, 9, 8

Count each size:

Size 7: 1 time

Size 8: 3 times

Size 9: 4 times ← Most frequent

Size 10: 1 time

Size 11: 1 time

Mode: 9 (sold most often)

Example 5: Mean vs Median with Outliers

Salaries at a small company: $45k, $48k, $52k, $55k, $58k, $62k, $450k (CEO)

Mean: ($45 + $48 + $52 + $55 + $58 + $62 + $450) / 7 = $110k

Median: $55k (middle value)

The CEO's salary pulls the mean way up

Median better represents "typical" employee salary

Quick Fact

The word "average" comes from the Arabic "awar," meaning damage or loss in maritime trade. When cargo was jettisoned to save a ship, losses were shared proportionally among merchants – this shared loss calculation was called "averaging." The mathematical sense emerged in the 17th century.

Frequently Asked Questions

How do I calculate average?

Add up all the numbers, then divide by how many numbers you have. For 10, 20, 30: sum is 60, count is 3, so average is 60/3 = 20.

What if there are two modes?

Your dataset is bimodal (two modes) or multimodal (more than two). Both values are equally "most frequent." If all values appear the same number of times, there's no mode.

Why is my median different from the mean?

They measure different things. Mean is pulled by outliers; median isn't. In skewed data (like salaries), median is often lower than mean because a few high values inflate the average.

What does standard deviation tell me?

It measures how spread out your data is. Low standard deviation means values cluster near the mean. High standard deviation means they're spread out. For normal distributions, 68% of values fall within one standard deviation of the mean.

Can I calculate average with negative numbers?

Yes. Negative numbers are included in the sum. For -5, 0, 5: sum is 0, count is 3, mean is 0. The math works the same.

How many numbers do I need?

Technically one, but averages are most meaningful with at least 3-5 values. The more data points, the more reliable your average becomes.

When should I use median instead of mean?

Use median when your data has outliers or is skewed. House prices, salaries, and reaction times often use median because extreme values distort the mean. The median tells you what's "typical" – half the values are above it, half below.

What's the difference between variance and standard deviation?

Variance is the average squared distance from the mean. Standard deviation is the square root of variance. Standard deviation is more interpretable because it's in the same units as your original data. If your data is in dollars, standard deviation is in dollars; variance is in "dollars squared."

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