Mean, Median, Mode, Range Calculator

Find the arithmetic mean (average), median middle value, statistical mode(s), and range spread for any dataset with sorted data and step-by-step mathematical solutions.

Please provide numbers separated by comma to calculate

• Enter raw numbers separated by commas, spaces, tabs, semicolons, or newlines.

• Click Calculate to instantly generate the sorted sequence, average, middle element, frequency mode, range, and quartiles.

• Choose a quick preset below to test various data shapes (even/odd counts, decimals, multimodal sets).

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Dataset Values (separated by commas, spaces, or lines):

Comprehensive Guide to Mean, Median, Mode, and Range

Core mathematical definitions, geometric intuition, comparative trade-offs, and worked examples.

1Understanding Central Tendency & Dispersion

In statistical data analysis, Central Tendency refers to the central or representative point of a distribution. While the Mean, Median, and Mode all capture this center, each behaves differently under skewed data and outliers:

Mean (Arithmetic Average)

Computed by summing all values and dividing by the count. Highly sensitive to extreme outliers and asymmetric tails.

Median (Middle Score)

The exact middle number in a sorted sequence. Resistant to outliers and ideal for skewed distributions (such as household income and real estate prices).

Mode (Most Frequent)

The value that appears most often. The only measure of central tendency applicable to nominal and categorical data.

Range (Spread)

The difference between the maximum and minimum observations. Measures the total breadth of the dataset.

2Mathematical Formulations & Definitions

Arithmetic Mean Formula:

x̄ = (x₁ + x₂ + ... + xₙ) / n = [ Σ xᵢ ] / n

Median Position Formula:

Odd n: Position = (n + 1) / 2 | Even n: Average of positions (n/2) and (n/2 + 1)

Range Formula:

Range = x_max - x_min

3Worked Example: Dataset [10, 2, 38, 23, 38, 23, 21]

Let us walk through the manual step-by-step resolution of the default dataset:

Sort: Order the 7 values from lowest to highest: 2, 10, 21, 23, 23, 38, 38.
Sum & Mean: Total summation = 2 + 10 + 21 + 23 + 23 + 38 + 38 = 155. Divide by count (7): 155 / 7 ≈ 22.1429.
Median: Since n = 7 (odd), the middle element is at index (7 + 1) / 2 = 4th position, which is 23.
Mode: Both 23 and 38 appear twice (frequency 2), so the dataset is Bimodal (23, 38).
Range: Maximum (38) minus Minimum (2) = 36.

Frequently Asked Questions

Can a dataset have more than one mode?

Yes. If two values share the highest frequency, the dataset is bimodal. If three or more share it, it is multimodal. If every value appears the exact same number of times (e.g. all appear once), the dataset has No Mode.

Why is the Median preferred over the Mean when analyzing home prices?

In real estate, a few multi-million-dollar mansions can heavily pull the average (mean) upwards, giving a false impression of what a typical house costs. The median reflects the true middle of the market.

How does a single outlier affect the range?

The range depends entirely on the single lowest and single highest values. A single extreme outlier (e.g., typing 1,000 instead of 10) will drastically inflate the range, which is why the Interquartile Range (IQR) is often reported alongside it.

What happens if I calculate mean and median for a single number?

For a dataset with n = 1 (e.g., [42]), the Mean = 42, Median = 42, Mode = 42, Min = 42, Max = 42, and the Range = 0.