Find the mean, median, and mode of ages across 50 employees at a company.
When data is grouped into class intervals (like "marks 0–10", "10–20", and so on) rather than listed as individual values, finding the mean, median, and mode needs different formulas than for raw data — since you no longer know the exact value of each observation, only which range it falls in.
<strong>Mean</strong> uses each class's midpoint as a stand-in for every value in that class. <strong>Median</strong> locates the class containing the middle observation, then estimates its exact position within that class using linear interpolation based on cumulative frequency. <strong>Mode</strong> identifies the class with the highest frequency (the modal class), then estimates the most likely value within it based on how its frequency compares to its neighbors.
This tool assumes classes are continuous, non-overlapping, and of equal width — the standard setup these formulas (and most textbook problems) are built around.
Grouped data doesn’t record individual values — only which class each observation falls into. The midpoint is the best available estimate of a typical value in that class, assuming observations are roughly evenly spread across it.
The class interval with the highest frequency. The mode formula then adjusts within that class based on how much higher its frequency is than the classes immediately before and after it — a modal class flanked by much smaller neighbors gives a mode closer to its center, while one with a similarly-sized neighbor shifts the estimate toward that side.
These formulas assume equal-width classes throughout — the mode formula in particular uses one shared class width ‘h’. Mixed-width classes need a different approach and aren’t supported here.
They measure "the middle" in different ways, and for anything other than a perfectly symmetric distribution, they won’t coincide. As a rule of thumb, mode ≈ 3×median − 2×mean for moderately skewed data — a useful sanity check, though not an exact relationship.