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Which statement about a "less than" cumulative frequency table is FALSE?

Class 10StatisticsStatistics and Probability
  • AThe entries never decrease as you move down the table
  • BThe final entry equals the total frequency n
  • CA class frequency is found by subtracting the previous entry from the current one
  • DThe entry against "less than 30" counts only the observations lying in the class 20–30

Step-by-Step Solution

"Less than 30" counts EVERY observation below 30, that is all the classes up to and including 20–30 added together — not just the last class. The other three statements are simply properties of a running total.
Answer: D) The entry against "less than 30" counts only the observations lying in the class 20–30

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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