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The empirical relationship between the three measures of central tendency is given by ____.

Class 10StatisticsStatistics and Probability
  • A3 Median = Mode + 2 Mean
  • B3 Mean = Mode + 2 Median
  • CMode = Mean + Median
  • D2 Median = Mode + Mean

Step-by-Step Solution

The empirical relation is Mode = 3 Median − 2 Mean, which rearranges to 3 Median = Mode + 2 Mean.
Answer: A) 3 Median = Mode + 2 Mean

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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