Question Bank • QB_EM_122 NAT • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Mean, median, mode and standard deviation

Question Statement:

For a moderately skewed frequency distribution, the mean is $45$ and the median is $42$. Using Karl Pearson's empirical formula, calculate the mode of the distribution.

Answer Key:

36

Step-by-Step Solution & Explanation

Karl Pearson's empirical relationship is: $\text{Mode} = 3(\text{Median}) - 2(\text{Mean})$ $\text{Mode} = 3(42) - 2(45) = 126 - 90 = 36.0$
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