Median Calculator

Calculate median, quartiles, and interquartile range (IQR) for your data set. Fast and accurate statistical analysis tool.

Calculate Median & Quartiles

Separate numbers with commas or spaces. Data will be automatically sorted.

Median & Quartile Formulas

Median

Middle value when data is sorted

Example: [1,3,5,7,9] → Median = 5. For even count, average the two middle values.

Quartiles (Q1, Q3)

Q1 = 25th percentile, Q3 = 75th percentile

Q1 is median of lower half, Q3 is median of upper half of the data.

IQR (Interquartile Range)

IQR = Q3 - Q1

Measures the spread of the middle 50% of data. Used to detect outliers.

How to Use This Calculator

1

Choose Your Data

Enter your numbers separated by commas or spaces. The calculator will automatically sort them.

2

Calculate Statistics

Click Calculate to get median, quartiles (Q1, Q3), min, max, and IQR for your data set.

3

Interpret Results

Median is the middle value. Q1 and Q3 divide data into quarters. IQR shows the spread of middle 50%.

4

Use for Analysis

Median is better than mean for skewed data. IQR helps identify outliers using the 1.5×IQR rule.

Example Calculations

Odd Number of Values

Find median of: 3, 7, 9, 15, 21

Solution: Sorted: [3,7,9,15,21]. Median = 9

The middle value in an odd-sized dataset.

Even Number of Values

Find median of: 2, 4, 6, 8

Solution: Average of 4 and 6 = 5

For even count, average the two middle values.

Quartiles & IQR

Data: 1, 3, 5, 7, 9, 11, 13

Solution: Q1=3, Median=7, Q3=11, IQR=8

IQR = Q3 - Q1 = 11 - 3 = 8

Where Median Calculations Are Used

Income Analysis

Median income is more representative than average when data is skewed. Used in economic reports and salary surveys.

Real Estate Pricing

Median home prices better represent typical market values, avoiding distortion from extremely high or low prices.

Test Score Analysis

Analyze student performance distributions, identify grade ranges, and understand score spreads using quartiles.

Healthcare Data

Analyze patient metrics, treatment outcomes, and medical measurements where outliers shouldn't skew results.

Market Research

Understand customer behavior, pricing strategies, and market trends using robust statistical measures.

Outlier Detection

Use IQR to identify outliers in data. Values beyond Q1-1.5×IQR or Q3+1.5×IQR are potential outliers.

Frequently Asked Questions

What is standard deviation?

Median is the middle value in a sorted dataset. Half the values are below it and half are above it. It's less affected by outliers than the mean.

How is median different from mean?

Mean is the average (sum divided by count). Median is the middle value. Median is better for skewed data because extreme values don't affect it as much.

What are quartiles?

Quartiles divide data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 is the median, and Q3 (75th percentile) is the median of the upper half.

What is IQR used for?

IQR (Interquartile Range) measures the spread of the middle 50% of data. It's used to detect outliers: values below Q1-1.5×IQR or above Q3+1.5×IQR are potential outliers.

How do you find median with even numbers?

With an even number of values, there's no single middle value. Take the average of the two middle values. For example, in [2,4,6,8], median = (4+6)/2 = 5.

Why use median instead of average?

Use median when data is skewed or has outliers. For example, median income is more representative than average income because a few very high incomes don't skew the median.