How the median is calculated (formula + steps)

The median is the middle value of a dataset after you sort it. It’s one of the three classic measures of central tendency (mean, median, mode). The key idea: instead of adding everything up (like the mean), the median uses position.

Sort your dataset from smallest to largest. If your data is: 8, 1, 4, 10, 6, sorting gives: 1, 4, 6, 8, 10.

• If n is odd: the median is the value at position (n + 1) / 2.
• If n is even: the median is the average of the values at positions n/2 and (n/2 + 1).

Dataset: 1, 4, 6, 8, 10 has n = 5. The middle position is (5 + 1) / 2 = 3. The 3rd value is 6. So the median is 6.

Dataset: 2, 4, 7, 9 has n = 4. The two middle positions are n/2 = 2 and n/2 + 1 = 3. The two middle values are 4 and 7. Median = (4 + 7) / 2 = 5.5.

Suppose you track delivery time (minutes): 12, 13, 11, 12, 200. The mean is pulled up by 200, but the median is the middle after sorting: 11, 12, 12, 13, 200 → median = 12. That’s why median is common for skewed data (income, prices, response times).

Examples you can copy (homework-friendly)

Scores: 72, 90, 83, 83, 95, 68, 77
Sorted: 68, 72, 77, 83, 83, 90, 95
n = 7 (odd) → middle position (7+1)/2 = 4 → median = 83.

Expenses: 1200, 950, 1100, 2400, 1000, 1050
Sorted: 950, 1000, 1050, 1100, 1200, 2400
n = 6 (even) → middle values = 1050 and 1100 → median = (1050+1100)/2 = 1075.

Numbers: -4, -1, 2, 9, 0
Sorted: -4, -1, 0, 2, 9 → median = 0.

Numbers: 5, 5, 5, 10, 10
Sorted: 5, 5, 5, 10, 10 → median = 5. Duplicates are normal and should usually be kept.

Behind the scenes (simple logic)

This tool follows the exact textbook definition of median:

• Parse your input into a list of numbers (commas/spaces/new lines all work).
• Optionally remove negatives or duplicates if you choose those settings.
• Sort the remaining values from low to high.
• If the count is odd, pick the middle value.
• If the count is even, average the two middle values.

The “Steps” box shows the sorted list, the middle index(es), and the final median formula so you can screenshot it for homework or reports.

• Skewed distributions (income, home prices, response times, social followers).
• Data with occasional extreme values (one huge number among typical ones).
• When you want the “typical middle” rather than the arithmetic average.

• When data is roughly symmetric and outliers are rare.
• When you need mean for other formulas (variance, standard deviation).

Median Calculator FAQs

• What is the median in simple words?

  The median is the middle number after sorting your list. Half the values are below it and half are above it (or as close as possible when there’s an even count).

• Why is median better than mean sometimes?

  Median isn’t heavily affected by extreme values. If one number is wildly large or small, the mean shifts a lot, but the median often stays close to the typical values.

• How do you find the median with an even number of values?

  Sort the list, take the two middle values, and average them. Example: 2, 4, 7, 9 → (4 + 7) / 2 = 5.5.

• Can the median be a decimal?

  Yes. If there’s an even number of values, the average of the two middle values can be a decimal.

• Should I remove duplicates?

  Usually no. Duplicates represent repeated measurements and belong in the dataset. Remove duplicates only if you’re intentionally working with unique values.

• What if my data includes text or extra symbols?

  This calculator tries to extract valid numbers from your input. If it can’t find at least one number, it will ask you to fix the input.

• Is median the 50th percentile?

  Yes—conceptually. The median is the value that splits the dataset so that about 50% of observations are below and 50% are above.

• Does this work for very large datasets?

  For most everyday lists (dozens to thousands of values), yes. Extremely large datasets are better handled in spreadsheets or statistical software, but the median logic is identical.