Mean, Median, Mode & Range Calculator

What Are Mean, Median, Mode, and Range?

These four statistics are the foundational tools of descriptive statistics, taught in every school curriculum worldwide. Together they give you a complete picture of any dataset — where the centre lies and how spread out the values are.

The mean is the arithmetic average, found by adding all values and dividing by the count. The median is the middle value when the data is sorted from smallest to largest. The mode is the value that appears most often. The range is the gap between the largest and smallest value. Using all four prevents the misleading conclusions that can arise from any single statistic alone.

How to Calculate the Mean

The mean — also called the arithmetic average — is calculated by summing all values and dividing by the number of values.

Formula: μ = (x₁ + x₂ + … + xₙ) / n

Using the class test scores preset as a worked example: 85, 92, 78, 95, 88, 76, 91, 83, 89, 74 (10 values).

1. Sum all values: 85 + 92 + 78 + 95 + 88 + 76 + 91 + 83 + 89 + 74 = 851.
2. Divide by the count: 851 ÷ 10 = 85.1.

The mean test score is 85.1. The mean is sensitive to outliers — one student scoring 150 would raise it to 91.4, even though every other student scored between 74 and 95.

How to Find the Median

The median is the value at the exact middle of a sorted dataset. It splits the data in half: 50% of values fall below it, 50% above.

1. Sort all values from smallest to largest.
2. If the count is odd, the median is the single middle value.
3. If the count is even, average the two middle values.

Example (class test scores, sorted): 74, 76, 78, 83, 85, 88, 89, 91, 92, 95. Count = 10 (even). The two middle values are the 5th (85) and 6th (88). Median = (85 + 88) ÷ 2 = 86.5.

Notice the median (86.5) is slightly higher than the mean (85.1) in this dataset. That tells us the lower scores are pulling the mean down more than the higher scores push it up.

How to Find the Mode

The mode is the value that appears most frequently. Unlike mean and median, a dataset can have no mode, one mode, or several modes.

• No mode: every value appears exactly once. Example: 1, 2, 3, 4, 5 — no value repeats.
• One mode (unimodal): 3, 6, 2, 5, 1, 4, 6, 3, 5, 2, 4, 6 — the value 6 appears three times, more than any other, so mode = 6.
• Multiple modes (multimodal): 3, 6, 2, 5, 1, 4, 6, 3, 5, 2, 4, 1 — the values 1, 3, 4, 6 each appear twice, so there are four modes.

The mode is especially useful for categorical data where arithmetic averages are meaningless — such as the most common shoe size ordered, the most frequent customer complaint category, or the most popular product in a store.

How to Calculate the Range

The range is the simplest measure of spread in a dataset.

Formula: Range = max − min

Using the class scores: max = 95, min = 74. Range = 95 − 74 = 21. The test scores span 21 points. The range is easy to interpret, but it is entirely driven by the two extreme values. A single unusually low or high value will inflate the range dramatically, making it a weak indicator of typical variability. For more robust measures of spread, consider standard deviation or the interquartile range.

When to Use Mean vs Median

Both the mean and median describe the centre of a dataset, but they respond very differently to extreme values. Choosing the wrong one leads to misleading conclusions.

The mean uses every value in its calculation. One very large or very small number can pull it far from where most data sits. Consider a street where nine houses sell for $250,000 and one house sells for $2,500,000. The mean sale price is $472,000 — potentially misleading for a buyer trying to understand typical prices. The median is $250,000 — far more representative of what most houses actually cost.

Use the mean when your data is roughly symmetric, contains no extreme outliers, and every value contributes meaningfully to the overall picture — such as temperature readings or standardised test scores.

Use the median when your data is skewed or contains outliers — income distributions, house prices, response times, and ages at retirement are classic examples where the median is preferred.

Measures of Central Tendency — Reference Table