Grouped Mode Calculator
The mode of a frequency table: the modal class named with its neighbours’ counts, the interpolation formula substituted symbol by symbol, and genuine ties refused with both classes called out.
Grouped Mode Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One modal class required — genuine ties refused
- Closed numeric classes; edge-peaks interpolate with less evidence
In short: Frequencies 4, 8, 10, 6 over classes 0–10 to 30–40: the modal class is 20–30 (f₁ = 10, flanked by f₀ = 8 and f₂ = 6), and the mode is 20 + ((10 − 8)/(2×10 − 8 − 6))×10 = 20 + (2/6)×10 ≈ 23.333333. The formula leans the answer toward the denser neighbour: the class below is fuller than the one above, so the mode drifts down from the midpoint 25. A tie — two classes at the top count — is refused with both named, because a mode worn by two classes is two answers wearing one page.
Formula
mode = L + ((f₁ − f₀) / (2f₁ − f₀ − f₂)) · h
f₁ is the modal class’s count, f₀ and f₂ its neighbours’ — the mode sits closer to the denser side.
Worked Example
- Find the peak. the class with the largest frequency is the modal class — printed with its neighbours.
- Lean. the formula slides the mode off the midpoint toward whichever neighbour is denser. Flat neighbours leave it centred.
- Refuse ties. two classes sharing the top count is a bimodal table — the page names both classes instead of secretly picking one.
4, 8, 10, 6: modal class 20–30, mode ≈ 23.333333 — pulled below the midpoint 25 because the lower neighbour (8) outcounts the upper (6). A flat 8-10-8 peak would land exactly on 25.
Strengths & Limits Of This Model
Where this engine is strong
- Neighbour counts printed, so the lean is auditable
- Ties refused with every class named, not resolved silently
Where it stops
- No kernel-density or smoothing view
- No multimodal report beyond the tie refusal
Practical Use Cases
Market data
price bands and demand peaks from published frequency tables
Demographics
modal age bands from census tables
Coursework
the substitution shown symbol by symbol
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 Mode Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why interpolate the mode inside a class?
Because grouping hides the individual values, but the neighbouring counts hint where the peak really leans. A class with 10 values, squeezed by 8 below and 6 above, probably holds its mass toward its fuller side — the formula turns that hint into an offset. It is an estimate built from the table’s shape, and the page prints the shape alongside it.
Why does the mode drift below 25 on the default table?
The midpoint 25 assumes the class is flat inside. The class BELOW holds 8 values, the one above only 6, so the peak’s shoulder is denser on the low side and the estimated mode slides to 23.333333. A symmetric 8-10-8 neighbourhood would leave it at exactly 25.
What happens with two equally frequent classes?
Refused, with both classes named. Two shared champions is a bimodal table: quoting one “the” mode would be fabrication by omission. The grouped formula also needs a unique peak — its denominator compares one neighbourhood, not two.
What about the first or last class being modal?
The formula still works with a missing neighbour treated as zero, but the lean becomes one-sided and the estimate weaker — the page says when the modal class sits at an edge. Boundary peaks are real; their interpolation just carries less evidence.
How is this different from the raw-list mode?
The math page counts exact repeated values; this page cannot see values at all — only classes. A raw table’s mode is a value; a grouped table’s mode is an interpolated position inside the fullest class. Different data state, different machinery, and the two pages cross-reference rather than overlap.
Can the mode land outside its class?
No. The fraction (f₁ − f₀)/(2f₁ − f₀ − f₂) is always between 0 and 1 whenever the counts are non-negative and f₁ is the strict maximum — which is exactly why ties are refused before the formula runs.
Why is the mode useful at all with grouped data?
Because it is the only average that answers “where is the crowd?” rather than “where is the balance?”. Income tables, age pyramids and demand curves are usually quoted by their modal band, and the interpolated mode sharpens the band to a position.
Does the denominator ever vanish?
Only when f₀ = f₁ = f₂ — a flat plateau of three equal classes, which is a three-way tie and refused with all three named before the division could happen.