Mode begins at the frequency peak
The modal class is the class with greatest ordinary frequency. Its position, not its class limits, determines the three frequencies used in the formula.
Learning goals
- Identify the modal class and neighbouring frequencies.
- Apply the grouped-data mode formula correctly.
- Convert inclusive class limits to continuous boundaries when required.
Concept lesson
Ordinary frequency and class width
Use the ordinary frequency column to find its maximum. Class width h is the difference between continuous boundaries of the modal class.
Modal class and neighbours
After locating the greatest frequency, label it f1; label the preceding class frequency f0 and succeeding class frequency f2. Use no cumulative-frequency column.
Grouped mode formula
Mode=l+[(f1-f0)/(2f1-f0-f2)]h, where l is the modal class's continuous lower boundary. Preserve the frequency positions before simplifying.
Populate the mode formula by position
Circle the maximum ordinary frequency, draw arrows to the preceding and succeeding rows, write l, h, f0, f1 and f2 in a parameter box, then substitute once.
Inclusive-to-continuous conversion
For inclusive classes such as 1-3, 4-6, find half the gap between 3 and 4, subtract it from lower limits and add it to upper limits; use the resulting lower boundary and width.
Frequency-peak scan
Ignore class magnitudes and cumulative totals; identify the largest ordinary frequency and report both the modal interval and requested lower or upper limit.
Parameter-box audit
Fill l, h, f0, f1 and f2 with row labels before substitution; verify the result lies within the modal class boundaries.
Boundary decision
Check whether successive limits meet. If inclusive classes have a gap, calculate the half-gap correction and rewrite only the boundary values needed for l and h.
Mode workflow under table variations
Compare exclusive and inclusive tables, identify the same frequency-position logic, apply boundary correction only where needed, and validate each result inside its modal class.
Mode answer protocol
State the modal class, list l, h, f0, f1 and f2, substitute in the formula and confirm the mode lies within the modal interval.
Grouped-mode mastery
Identify modal classes in two table formats, convert inclusive boundaries, calculate grouped mode and validate its interval.