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Mean Median Mode Calculator

Mean, Median, and Mode are the three fundamental pillars of descriptive statistics representing central tendency. This free Mean Median Mode Calculato

Mathematics
Enter your dataset to calculate all major summary statistics.
Formula & Methodology
Mean = (Σx) ÷ n Median = middle number of sorted dataset Mode = most frequently occurring number(s) Range = Maximum - Minimum

To compute all three measures from a dataset: 1. Mean: Sum all numbers and divide by the count n. 2. Median: Order numbers from smallest to largest and identify the middle value (or average the two center numbers for even counts). 3. Mode: Tally occurrences and identify the number(s) with the highest frequency. 4. Range: Subtract the smallest number from the largest number.

Three Measures of Central Tendency

Mean: 13.14 | Median: 12 | Mode: 12

Overview

Mean, Median, and Mode are the three fundamental pillars of descriptive statistics representing central tendency. This free Mean Median Mode Calculator evaluates all three metrics concurrently, alongside statistical range, minimum, and maximum boundaries.

Evaluating all three metrics together reveals the underlying shape of your data: when mean, median, and mode are identical, the distribution is symmetrical; when the mean diverges significantly from the median, the distribution is skewed by outliers.

Worked Examples

Example 1: Comprehensive Analysis of [5, 8, 12, 12, 15, 18, 22]

Dataset: 5, 8, 12, 12, 15, 18, 22 (n = 7)

  1. Mean: (5 + 8 + 12 + 12 + 15 + 18 + 22) ÷ 7 = 92 ÷ 7 = 13.14.
  2. Median: 7 items (odd). Middle number at position 4 is 12.
  3. Mode: 12 appears twice, all others appear once. Mode = 12.
  4. Range: 22 - 5 = 17.
Final Answer: Mean: 13.14 | Median: 12 | Mode: 12 | Range: 17

Example 2: Symmetrical Distribution [10, 20, 20, 30]

Dataset: 10, 20, 20, 30 (n = 4)

  1. Mean: (10 + 20 + 20 + 30) ÷ 4 = 80 ÷ 4 = 20.
  2. Median: (20 + 20) ÷ 2 = 20.
  3. Mode: 20.
Final Answer: Mean: 20 | Median: 20 | Mode: 20 (Symmetric)

Example 3: Skewed Dataset with Large Outlier [1, 2, 2, 3, 50]

Dataset: 1, 2, 2, 3, 50

  1. Mean = 58 ÷ 5 = 11.60 (pulled high by 50).
  2. Median = 2 (unaffected by 50).
  3. Mode = 2.
Final Answer: Mean: 11.60 | Median: 2 | Mode: 2 (Right-Skewed)

How to Use This Calculator

  1. Enter your dataset separated by commas or spaces into the box.
  2. Click "Calculate" to generate the comprehensive statistical profile.
  3. Review the Mean, Median, Mode, Range, and boundaries in the summary table.
  4. Click "Reset" to analyze a new dataset.

Reference Table

DatasetMeanMedianModeRange
1, 2, 2, 32.002.0022
4, 8, 6, 5, 35.205.00No Mode5
5, 8, 12, 12, 15, 18, 2213.1412.001217
10, 20, 20, 3020.0020.002020
1, 2, 2, 3, 5011.602.00249

Frequently Asked Questions

What does it mean when the mean is greater than the median?
When the mean is substantially higher than the median, the dataset is right-skewed (positively skewed) by high outliers pulling the arithmetic average upward.
Which of the three measures is best to use?
It depends on data distribution: use the Mean for symmetric data without outliers, the Median for skewed data or financial incomes, and the Mode for categorical choices or retail sizing.
Can all three measures be identical?
Yes. In any perfectly symmetrical unimodal distribution, the mean, median, and mode are identical.
What happens if every value occurs only once?
The mean and median calculate normally, while the mode is reported as "No Mode".
How does dataset sample size affect these metrics?
Larger sample sizes reduce the impact of individual anomalies on the mean and provide a more stable estimate of the true population center.

Related Calculators

🧮Mean Calculator🧮Median Calculator🧮Mode Calculator🧮Range Calculator
Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Integrated descriptive statistical aggregation per NIST guidelines.