Question Bank • QB_EM_ADV_068
MCQ • 1 Mark
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Mean, median, mode and standard deviation
Question Statement:
For a moderately skewed unimodal frequency distribution, Karl Pearson's empirical relationship between mean, median, and mode is given by:
Options:
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(A) $\text{Mode} \approx 3\,\text{Median} - 2\,\text{Mean}$
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(B) $\text{Mode} \approx 2\,\text{Median} - 3\,\text{Mean}$
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(C) $\text{Mode} \approx 3\,\text{Mean} - 2\,\text{Median}$
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(D) $\text{Mode} \approx \text{Mean} - 3\,\text{Median}$
Step-by-Step Solution & Explanation
Karl Pearson's classical empirical rule relates central tendency metrics as:
$\text{Mean} - \text{Mode} \approx 3(\text{Mean} - \text{Median})$
Rearranging to express Mode:
$\text{Mode} \approx \text{Mean} - 3\,\text{Mean} + 3\,\text{Median} = 3\,\text{Median} - 2\,\text{Mean}$
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