Grouped Median Calculator
The median when the raw values are gone: classes and frequencies in, the cumulative table built, the median class named, and the interpolation L + ((n/2 − CF)/f)·h substituted term by term from your own table.
Grouped Median Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Closed numeric classes only; 2 to 60 classes
- Even-spread-within-class assumption stated, not checkable
In short: Classes 0–10, 10–20, 20–30, 30–40 with frequencies 4, 8, 10, 6 hold n = 28 values, so the median sits at position 14. The cumulative frequencies run 4, 12, 22, 28 — the first class to reach 14 is 20–30, so that is the median class. Inside it: median = 20 + ((14 − 12)/10)×10 = 22. Every symbol in that formula is from your table — L = 20 is the class’s lower edge, CF = 12 the count below it, f = 10 its own count, h = 10 its width. The raw values are gone; the table still knows where the middle lives.
Formula
median = L + ((n/2 − CF) / f) · h
L is the median class’s lower edge, CF the count below it, f the class’s own frequency, h its width — the formula spreads the shortfall evenly across the class.
Worked Example
- Build the ladder. cumulative frequencies, class by class — the table printed in full.
- Find the class. the first cumulative count to reach n/2 owns the median position.
- Interpolate. the formula assumes values spread evenly inside the class, so the shortfall (n/2 − CF) buys that fraction of the width h.
f = 4, 8, 10, 6: n = 28, half = 14. CF ladder 4, 12, 22, 28 — median class 20–30. median = 20 + ((14 − 12)/10)×10 = 22 exactly.
Strengths & Limits Of This Model
Where this engine is strong
- The cumulative ladder and the median class are printed before any formula
- Every symbol substituted from your own table
Where it stops
- No ogive or percentile interpolation beyond the median
- No open-ended classes
Practical Use Cases
Published tables
census income bands, age pyramids, exam grade boundaries — raw rows gone, classes left
Reports
the median of a histogram, honestly interpolated
Coursework
every substitution symbol named
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Grouped Median Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why interpolate at all?
Because the table threw the raw values away. All that survives is the count inside each class, so the formula assumes those values lie evenly across the class and slices the class at the exact position needed. The assumption is stated, visible, and the only honest move left.
What do L, CF, f and h each come from?
L is the median class’s LOWER edge (not the lower boundary of the data); CF is the cumulative frequency BELOW that class; f is the class’s own count; h is the class width. The page substitutes each one from your table into the printed working — no symbol stays abstract.
How is the median class chosen?
The first class whose cumulative frequency reaches n/2. Position 14 on the default table first passes at 22, which belongs to 20–30. Even when n/2 lands exactly on a boundary, the class STARTING there is the one the formula wants.
How accurate is a grouped median?
It depends on the even-spread assumption inside the median class. With narrow, well-filled classes the error is small; with one wide sparse class it can be larger. The honest comparison is the raw-list median — the math page’s — whenever the raw data still exists.
What classes are legal?
Numeric intervals like 10-20, contiguous and increasing, with positive integer counts. The page parses the dash, checks the ladder is monotone, and refuses gaps or overlaps with the offending pair named.
Why does the formula use n/2 and not (n+1)/2?
Convention for grouped data: the interpolation targets the n/2 position of the COUNT, treating the class as a continuous strip. The (n+1)/2 flavour belongs to raw-list order statistics, where individual positions exist. The two conventions meet when the class is a single value.
Can this page take the raw values instead?
No — that question has its own page. The math median works on the list you still hold; this page exists for the moment the list is gone and only the table survives. The two pages cross-reference each other’s ground.
What about open-ended classes like 50+?
Refused for the median when the median class needs a width to interpolate across — an open class has no h. If the median lands in a closed class the open tail above is harmless, but the page asks for closed classes to keep the working honest.