What is the difference between mean, median, and mode?

The mean is the arithmetic average (sum ÷ count). The median is the middle value in a sorted list. The mode is the value that appears most often. All three are measures of central tendency but respond differently to outliers — the median is more robust when extreme values are present.

When should I use median instead of mean?

Use the median when your data has outliers or is skewed. For example, household income data includes a few very high earners that inflate the mean. The median gives a better picture of the 'typical' value in such cases.

What does 'no mode' mean?

If every value in the list appears exactly once, there is no unique mode. This calculator shows the mean in that field as a fallback.

How is the range calculated?

Range = maximum value − minimum value. It measures the spread of your data. A large range indicates high variability; a small range indicates values are clustered together.

Average Calculator

An average calculator lets you instantly compute the three classic measures of central tendency — mean, median, and mode — alongside supporting statistics like count, sum, and range. Whether you’re analyzing test scores, comparing prices, or working on a statistics assignment, this tool handles the arithmetic so you can focus on interpretation.

What Is an Average?

In everyday language, “average” almost always means the arithmetic mean — the sum of a set of values divided by how many values there are. In mathematics and statistics, however, “average” is an umbrella term that covers several different measures:

Mean (arithmetic average) — the sum of all values divided by the count.
Median — the middle value when the data is sorted from smallest to largest.
Mode — the value that appears most often.

Each measure describes the “center” of a data set differently, and each is more useful in certain situations.

How to Calculate Mean, Median, and Mode

Arithmetic Mean

The formula for arithmetic mean is:

Mean = (x₁ + x₂ + … + xₙ) / n

where n is the number of values.

Example: For the data set {4, 8, 15, 16, 23, 42}:

Sum = 4 + 8 + 15 + 16 + 23 + 42 = 108
Count = 6
Mean = 108 / 6 = 18

Median

Sort the values from smallest to largest.
If n is odd, the median is the value in position (n + 1) / 2.
If n is even, the median is the average of the two middle values.

Example: For {4, 8, 15, 16, 23, 42} (already sorted, n = 6):

Middle positions: 3rd (15) and 4th (16)
Median = (15 + 16) / 2 = 15.5

Mode

Count how often each value appears. The value with the highest count is the mode. If no value repeats, there is no mode.

Example: For {2, 3, 3, 5, 7, 3, 8}:

3 appears 3 times — the most frequent value.
Mode = 3

Range

Range = Maximum − Minimum

For {4, 8, 15, 16, 23, 42}: Range = 42 − 4 = 38

Worked Examples

Example 1 — Test Scores

A class scored: 72, 85, 90, 68, 74, 85, 91, 78

Mean: (72 + 85 + 90 + 68 + 74 + 85 + 91 + 78) / 8 = 643 / 8 = 80.375

Median: Sorted: 68, 72, 74, 78, 85, 85, 90, 91 → Middle pair: 78 and 85 → (78 + 85) / 2 = 81.5

Mode: 85 appears twice (the only repeated value) → 85

Range: 91 − 68 = 23

The mean and median are close (about 80–81), suggesting the data is fairly symmetrical.

Example 2 — House Prices (Effect of an Outlier)

House prices in a neighborhood (thousands): 250, 270, 265, 280, 260, 1100

Mean: 2425 / 6 ≈ ** $404k** — pulled up significantly by the$ 1.1M outlier.

Median: Sorted: 250, 260, 265, 270, 280, 1100 → (265 + 270) / 2 = $267.5k

Here the median is far more representative of a “typical” home than the mean.

Example 3 — Shoe Sizes at a Store

Sizes sold in one day: 8, 9, 10, 10, 10, 11, 12, 9, 10

Mode = 10 — the store should stock more size 10 than any other.

When to Use Mean vs. Median vs. Mode

Measure	Best used when…
Mean	Data is symmetric, no major outliers
Median	Data is skewed or has outliers
Mode	You need the most common value (e.g., clothing sizes, survey responses)

Common Mistakes

Using mean with skewed data. Income, house prices, and other right-skewed distributions have means that overstate the typical value. Prefer the median.
Confusing median position with median value. For {1, 2, 3, 4}, the median is 2.5 (average of 2 and 3), not 3.
Assuming there is always one mode. Data can have multiple modes (bimodal, multimodal) or no mode at all.
Ignoring the range. Two data sets can have the same mean but very different spreads — always report the range or standard deviation alongside the average.

Frequently Asked Questions

Can I average percentages? You can average percentages if each percentage applies to the same base quantity. If the bases differ, you need a weighted average instead.

What is a weighted average? A weighted average multiplies each value by a weight (its relative importance) before summing and then divides by the total weight. Example: if exam 1 counts 40% and exam 2 counts 60%, the final grade = (score₁ × 0.4 + score₂ × 0.6).

Why is the mean sensitive to outliers? The mean uses every value equally, so an extreme value shifts the sum substantially. The median only depends on order, so extreme values don’t move it much.

What is the geometric mean? The geometric mean is the nth root of the product of all values. It is used for growth rates and ratios (e.g., compound interest, population growth).