Grouped data hides its average, its "most common" value and its middle value inside class intervals. This notebook rebuilds every method NCERT gives you — direct, assumed-mean, step-deviation, modal class, median class, and the ogive — as tables you can edit and watch redraw live.
Every class interval is represented by its class mark xi. Edit the frequencies below and compare all three NCERT methods — Direct, Assumed Mean, and Step-Deviation. They should always land on the same mean.
| Class | xi | fi | fixi | di=xi−a | fidi | ui=di/h | fiui |
|---|---|---|---|---|---|---|---|
| Total | — | — | — |
The modal class is simply the class with the highest frequency. The exact mode sits somewhere inside it, pulled toward whichever neighbour has more observations. Change the frequencies and watch the modal class — and the formula's substitution — update.
| Class interval | fi |
|---|
Build the "less than" cumulative frequency column, locate n/2, and find the first class whose cumulative frequency reaches or passes it — that's the median class.
| Marks | fi | cf |
|---|---|---|
| Total n = | — |
Plot the "less than" ogive (rises, plotted at upper limits) and the "more than" ogive (falls, plotted at lower limits). They cross at a single point — its x-coordinate is the median, no formula required. Uses the same data as the Median tab.
For reasonably moderately-skewed data, NCERT gives a shortcut linking all three measures:
| Value | |
|---|---|
| Mean (x̄) | |
| Mode | |
| Median (from formula) | |
| Median (empirical estimate) |