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For a grouped distribution, n = 72 and the median class is 20–30 with l = 20, cf = 30, f = 16, h = 10. The median is ____.

Class 10StatisticsStatistics and Probability
  • A20.38
  • B22.50
  • C25.00
  • D23.75

Step-by-Step Solution

Median = 20 + 10 × (36 − 30)/16 = 20 + 60/16 = 20 + 3.75 = 23.75. (20.38 is the result of omitting h = 10 from the formula.)
Answer: D) 23.75

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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