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For a grouped distribution, n = 35 and the median class is 10–15 with l = 10, cf = 10, f = 8, h = 5. The median is ____.

Class 10StatisticsStatistics and Probability
  • A10.94
  • B14.69
  • C13.75
  • D15.63

Step-by-Step Solution

Median = 10 + 5 × (17.5 − 10)/8 = 10 + 37.5/8 = 10 + 4.69 = 14.69. (10.94 is what you get if you leave out the factor h = 5.)
Answer: B) 14.69

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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