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The less than ogive shows the marks of 80 students. Read the median from the ogive, and find how many students scored less than 40.

Class 10StatisticsStatistics and Probability
  • AMedian 40; 60 students
  • BMedian 30; 20 students
  • CMedian 35; 60 students
  • DMedian 30; 60 students

Step-by-Step Solution

. The ogive reaches cumulative frequency at , so the median is . At the cumulative frequency is , so students scored less than .
Answer: D) Median 30; 60 students

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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