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A distribution has classes 0–5, 5–10, 10–15, 15–20, 20–25 with cumulative frequencies 4, 10, 18, 27, 35. For the median formula, the correct values of l, cf and f are ____.

Class 10StatisticsStatistics and Probability
  • Al = 5, cf = 4, f = 6
  • Bl = 10, cf = 18, f = 8
  • Cl = 15, cf = 18, f = 9
  • Dl = 10, cf = 10, f = 8

Step-by-Step Solution

n = 35 so n/2 = 17.5, and the first cf ≥ 17.5 is 18 — the class 10–15. Hence l = 10, the cf of the preceding class is 10, and f = 18 − 10 = 8. (cf = 18 is the cumulative frequency of the median class itself; l = 15 belongs to the next class.)
Answer: D) l = 10, cf = 10, f = 8

Key idea: Median for grouped data

**Step 1**: build cumulative frequency (cf) column.
**Step 2**: find n/2 (half the total frequency).
**Step 3**: locate the **median class** — the FIRST class whose cumulative frequency ≥ n/2.
**Step 4**: Apply formula.

**Median formula**:
**Median = l + h × (n/2 − cf) / f**

Where:
- l = lower limit of median class
- h = class width
- n = total frequency
- cf = cumulative frequency of class BEFORE median class
- f = frequency of median class

The formula uses linear interpolation within the median class to find where the n/2-th item falls.

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