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A 'less than' ogive passes through the point (60, 25) where 25 = n/2. From this, the median of the data is ____.

Class 10StatisticsStatistics and Probability
  • A120
  • B60
  • C66
  • D54

Step-by-Step Solution

Reading the median from a 'less than' ogive: the -value where cumulative frequency equals n/2 is the median. Here that -value is 60.
Answer: B) 60

Key idea: Ogives — the cumulative frequency curve

**Less-than ogive**: plot points (upper limit of class, cf) for each class. Connect with smooth curve.

**More-than ogive**: plot points (lower limit of class, more-than-cf). Connect smoothly.

**Median from ogives**:
- Method A: From the less-than ogive, find where cf = . Drop perpendicular to -axis. The -coordinate is the median.
- Method B: Plot BOTH ogives on the same axes. Their intersection's -coordinate is the median.

**Empirical relationship** (rough): Mode ≈ 3 × Median − 2 × Mean. Useful sanity check, not rigorously true but often close.

**Frequency polygon vs ogive**: Polygon plots (class mark, frequency); Ogive plots (limit, cumulative frequency).

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