Class 10 Grouped Data: Mean, Median and Mode Explained
Mean, median and mode answer different questions. With grouped data, the exact individual values are usually unavailable, so the methods use information preserved by the intervals and frequencies.
Sources checked 2 October 2026 · original study guide · CBSE/NCERT context
Reference guide · Read at your own pace
Choose the measure
Swipe across the table to see all columns.
| Measure | Idea | Information to prepare |
|---|---|---|
| Mean | Weighted balance of the observations | Class marks and frequency × class mark |
| Median | Middle position after ordering | Cumulative frequencies and N/2 |
| Mode | Most concentrated region | Modal class and neighbouring frequencies |
A small original frequency table
Use intervals that include the lower boundary and exclude the upper boundary, so a value of 10 belongs in 10–20. Here N = 10.
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| Class | Frequency | Class mark | Cumulative frequency |
|---|---|---|---|
| 0–10 | 3 | 5 | 3 |
| 10–20 | 5 | 15 | 8 |
| 20–30 | 2 | 25 | 10 |
Compare the three calculations
Mean = (3 × 5 + 5 × 15 + 2 × 25)/10 = 14. This treats each group as concentrated at its midpoint, so it estimates the mean of the underlying observations.
For the median, N/2 = 5. Cumulative frequency first exceeds 5 in 10–20, the median class. With lower boundary 10, preceding cumulative frequency 3, class frequency 5 and width 10, median = 10 + [(5 − 3)/5] × 10 = 14.
The modal class is also 10–20. For these equal-width intervals, the grouped mode is 10 + [(5 − 3)/(2 × 5 − 3 − 2)] × 10 = 14. This example gives the same three estimates; that agreement is not a general rule.
A second distribution: the averages differ
For frequencies 2, 6, 1, N = 9. Mean = 125/9 ≈ 13.89. Median = 10 + [(4.5−2)/6]×10 ≈ 14.17. Mode = 10 + [(6−2)/(12−2−1)]×10 ≈ 14.44. All three use the same data but answer different questions. The midpoint mean and interpolated median/mode estimate unavailable individual values; the agreement in the first example was incidental.
Swipe across the table to see all columns.
| Class | Frequency | Class mark | Cumulative frequency |
|---|---|---|---|
| 0–10 | 2 | 5 | 2 |
| 10–20 | 6 | 15 | 8 |
| 20–30 | 1 | 25 | 9 |
Check the table before the formula
Sum frequencies yourself; do not confuse the number of classes with N. For median, use the cumulative frequency before the median class, not its own cumulative frequency. For mode, choose the largest frequency only when class widths are equal for the standard formula used here.
If you make a formula card, write the meaning of each symbol beside it. A correct formula with the wrong class frequency still gives the wrong answer. Keep the original intervals visible throughout the calculation.
Choose what to study next
Sources and scope
This is a focused learning resource, not a complete chapter or a prediction of board questions. Use your current syllabus and the paper-specific marking scheme for assessment requirements.
Frequently asked questions
Is the modal class itself the mode?
The modal class is an interval. The usual grouped-data formula estimates a value within that interval; report which one the question asks for.
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