Statistics & Probability calculator
Median Calculator
Find the median of raw data, frequency tables, and grouped data, then review quartiles, mean, mode, range, IQR, and the five-number summary in one clean median-first workflow.
Median calculator results
Your median will appear here
Enter your data and click Calculate.
Median
Raw-data and frequency-table results are exact for the values entered. Grouped-data outputs are estimates based on class intervals and cumulative frequency.
Calculator overview
Quick Median Calculator Overview
Use this median calculator to find the middle value of a data set, with sorting, even-count handling, grouped data support, and companion statistics. It helps compare median with mean, range, and count.
Enter a list or grouped data to calculate the median and supporting summary values.
Guide
Median Calculator Guide
Use this guide to understand what the median means, how quartiles are found, and why grouped-data results are estimated while raw-data and exact frequency results are not.
What This Calculator Does
This median calculator helps you find the median of raw data, exact frequency tables, and grouped data. It also calculates quartiles and common descriptive statistics such as mean, mode, range, IQR, and the five-number summary when you want them on the same page.
The page stays median-first, but it still covers the companion statistics users usually expect from a median finder, including a calculator for mean median mode and range style workflows.
What the Median Means
The median is the middle value of an ordered data set. It is also the second quartile, or Q2. Because it depends on position rather than the size of every value, it is often more resistant to outliers than the mean.
How to Find the Median
Start by sorting the data from smallest to largest. Then check whether the number of values is odd or even.
Quartiles and IQR
Quartiles divide ordered data into four parts. Q1 is the first quartile, Q2 is the median, and Q3 is the third quartile. The interquartile range, or IQR, is Q3 minus Q1.
This page uses the median-of-lower-half and median-of-upper-half method for consistency. When the data count is odd, the overall median is excluded from both halves before Q1 and Q3 are found.
Mean, Mode, and Range
Mean is the arithmetic average. Mode is the most frequent value, or values if the data is multimodal. Range is the maximum minus the minimum. Users often calculate these together because they describe center and spread from different angles.
Grouped Data Median
When only class intervals and frequencies are available, the median is estimated from cumulative frequency and the median class. The grouped-data mode applies the standard interpolation formula, which is why those results are labeled as estimates instead of exact values.
Equal-width, non-overlapping classes give the cleanest grouped-data workflow. If the original raw observations are available, the raw-data or frequency-table modes are more exact.
How to Use
- 1Choose the input mode
Select raw data, frequency table, grouped data, or the all-in-one companion stats mode.
- 2Enter your data
Paste a list, fill in value-frequency rows, or add grouped class intervals and frequencies.
- 3Click Calculate
Results stay hidden until you submit the calculator.
- 4Review the median first
Then compare quartiles, companion statistics, and the step-by-step work.
- 5Check the notes
Grouped-data estimates and quartile-method details are explained right in the result section.
Tips / Notes
- Always sort raw data before finding the median.
- Grouped-data results are estimates because the original raw positions are not fully known.
- Quartile methods can vary between calculators, so consistent rules matter.
- Median is often more resistant to outliers than the mean.
- Repeated values change the mode, but the median still depends on ordered position.
FAQ
Frequently Asked Questions
Clear answers about medians, quartiles, grouped data, and why software can disagree on Q1 and Q3.
What does the Median Calculator do?
It helps you find the median of raw data, frequency tables, and grouped data, while also calculating quartiles, IQR, mean, mode, range, and the five-number summary.
How do I find the median of a data set?
Sort the data first. If the count is odd, the median is the middle value. If the count is even, the median is the average of the two middle values.
What is the difference between median and mean?
The median is the middle value in ordered data. The mean is the arithmetic average. Median is often less affected by outliers than the mean.
How do I find Q1 and Q3?
This calculator uses the median-of-halves method. After sorting the data, Q1 is the median of the lower half and Q3 is the median of the upper half.
Can this calculator handle grouped data?
Yes. The grouped-data mode estimates the median, quartiles, mean, and mode from class intervals and frequencies, and labels those outputs clearly as estimates.
Why can quartiles differ between calculators?
Different calculators can use different quartile conventions. This page uses one consistent method and explains it so your Q1 and Q3 results are predictable.