M̃ Median Calculator

Find the median (middle value), Q1, Q3, interquartile range, and five-number summary. Robust to outliers — ideal for skewed income, housing, or test-score data.

The Middle Value That Survives Outliers

BrainyCalculators editorial insight — unique to this tool

Median home prices reported by NAR and Indian RERA dashboards describe the typical buyer better than mean because a few luxury sales skew averages upward. In even-count datasets, median is the average of the two central values — salary bands with 50 employees use this routinely. Unlike mean, median ignores the magnitude of extremes: one CEO earning 100× the staff does not move the median rupee.

When to use this calculator

Choose median for skewed income, housing, latency, or review scores when you want "what a typical case looks like." Use Mean when you need properties for variance or the data is symmetric.

Reference	Value	Context
US household income	Median < Mean	Census reports both
Home sale prices	Median preferred	NAR methodology
Server response times	Median P50	Outlier-resistant SLA
Even n dataset	Avg of 2 middles	e.g., 4 values

Not what you need? For "what % of values fall below X," use Percentile. For spread, use Standard Deviation — median alone says nothing about dispersion.

Need arithmetic or compound averages?

This page finds the median, quartiles, and IQR. For arithmetic, geometric, and harmonic means — including growth-rate averaging — use the Mean Calculator →

Data Set (comma or space separated)

What is the Median?

The median is the middle value when data is sorted. Half the observations fall below it and half above — unlike the mean, extreme outliers do not pull it. This calculator also reports Q1, Q3, IQR, and the five-number summary for box-plot and outlier analysis.

Use the median for skewed distributions: salaries, home prices, exam scores with a few very high values. When you need the most common value (e.g., most frequent shoe size or survey answer), use the Mode Calculator instead.

For the arithmetic average and when outliers are acceptable or symmetric, use the Mean Calculator. Median, mode, and mean are complementary — pick the measure that matches the question.

Median Formula

Odd count (n is odd)

Median = value at position (n + 1) / 2 after sorting

Even count (n is even)

Median = (value at n/2 + value at n/2 + 1) / 2

Interquartile Range

IQR = Q3 − Q1

How to Find the Median

1

Enter Your Numbers

Type numbers separated by commas or spaces. Order does not matter — the calculator sorts the data for you.
2

Sort the Data

Arrange all values from smallest to largest. The calculator does this automatically and shows the sorted list.
3

Find the Middle Value

For odd count, the median is the exact middle element. For even count, it is the average of the two middle elements.
4

Read Quartiles and IQR

Q1 is the median of the lower half, Q3 is the median of the upper half. IQR = Q3 − Q1 measures spread.

Worked Example

Data set: 1, 3, 3, 6, 7, 8, 9

Sorted: 1, 3, 3, 6, 7, 8, 9 (n = 7, odd)

Median = position 4 = 6

Lower half: 1, 3, 3 → Q1 = 3

Upper half: 7, 8, 9 → Q3 = 8

IQR = 8 − 3 = 5

How the Median Calculator Works

Formula, assumptions, and calculation steps for this statistics tool.

Methodology

Statistics calculators organize sample data, apply the selected descriptive or inferential formula, and report the statistic with interpretation.

Calculation Steps

Enter raw values or summary statistics.
Clean separators and count the sample size.
Apply the relevant statistic, probability, or confidence formula.
Display the result with context such as degrees of freedom, percentile, or strength.

Assumptions and Limits

Samples should be representative of the population being studied.
Normality or independence assumptions apply only where the selected method requires them.
Rounded results may differ slightly from spreadsheet software.

Frequently Asked Questions

What is the median?

The median is the middle value of a data set when sorted in order. It divides the data into two equal halves. Unlike the mean, it is not affected by extreme outliers, making it a reliable measure of central tendency for skewed data.

How do you find the median of an even data set?

When the count is even, there is no single middle value. Instead, take the average of the two middle values after sorting. For example, in {2, 4, 6, 8} the median is (4 + 6) / 2 = 5.

What is the interquartile range (IQR)?

The IQR is the difference between Q3 (75th percentile) and Q1 (25th percentile). It represents the spread of the middle 50% of your data and is used to identify outliers. Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are often considered outliers.

When should I use median instead of mean?

Use median when your data is skewed or contains outliers. For example, household income data is typically reported using the median because a small number of very high earners would inflate the arithmetic mean, making it unrepresentative of typical income.

Real-World Applications

💰

Income & Wealth Reporting

Median household income is used in economic reporting because it represents the "typical" household — unlike mean income, it is not skewed upward by the very wealthy.

🏠

House Price Analysis

Median house price is the standard metric in real estate market reports — more informative than mean price, which is distorted by a small number of ultra-luxury properties.

🏥

Healthcare Wait Times

Median wait time for a procedure better represents the experience of a typical patient than the mean, which is skewed upward by a few unusually long waits.

📊

Salary Benchmarking

HR professionals use median salary by role and industry for compensation benchmarking — the 50th percentile salary defines what half the market earns above and below.

🧪

Clinical Trials

Median overall survival (mOS) is the standard efficacy endpoint in oncology trials — the time by which 50% of patients have died — because survival data is right-skewed.

📈

Financial Data Analysis

Median PE ratio, median revenue growth, and median margins are preferred to means in financial screening — extreme outliers (distressed or hyper-growth companies) inflate means but not medians.

Common Mistakes

Forgetting to sort the data before finding the median

The median is the middle value of a sorted dataset — not the middle value in the original order. Forgetting to sort first produces the wrong result for any dataset that is not already in ascending order.

Incorrectly averaging for even-count datasets

For an even number of values, the median is the average of the two central values. Taking only the lower or upper central value (rather than averaging them) introduces a systematic error of half the gap between those values.

Assuming the median is always better than the mean

The median is more robust to outliers, but the mean is the correct measure when all values are equally important and the distribution is symmetric. For normal distributions, mean and median coincide — there is no practical difference.

Using the median for time series or aggregated data

Median is appropriate for cross-sectional data (observations at a single point in time). For time series, median can be misleading because it ignores trends — a trending series has a different median at different time windows.

Confusing median with the 50th percentile in grouped data

For grouped (binned) frequency data, the median must be estimated using the interpolation formula within the median class — not simply taking the middle group boundary. The exact median location requires the cumulative frequency approach.

Mean vs Median: When to Use Each

Situation	Preferred Measure	Reason
Symmetric distribution, no outliers	Either (mean preferred)	Mean uses all information
Right-skewed (e.g. income)	Median	Outliers inflate mean
Left-skewed (e.g. age at retirement)	Median	Low outliers deflate mean
Ordinal data (e.g. ratings)	Median	Mean requires interval scale
Normally distributed data	Mean	Mean = Median; mean has nicer math
Survival / time-to-event data	Median	Right-censored, not normally distributed

References

Tukey, J.W. Exploratory Data Analysis. Addison-Wesley, 1977.
Moore, D.S., McCabe, G.P., and Craig, B.A. Introduction to the Practice of Statistics. Freeman, 2017.
Casella, G. and Berger, R.L. Statistical Inference. Cengage, 2001.
US Census Bureau. Current Population Survey — Income, Poverty and Health Insurance in the United States. Census Bureau, 2024.
WHO. World Health Statistics 2024. World Health Organization, 2024.