Statistics
Measures of Central Tendency
IIT-JEE 1984
Grade 11
Question:
For a moderately skewed distribution, the empirical relation connecting mean, median and mode is:
(1) $\text{Mode} = 3\text{Median} - 2\text{Mean}$
(2) $\text{Mode} = 2\text{Median} - 3\text{Mean}$
(3) $\text{Mode} = 3\text{Mean} - 2\text{Median}$
(4) $\text{Mode} = \text{Median} + \text{Mean}$
Step-by-Step Solution
Key Concept: Recall Karl Pearson's empirical relation between the three measures of central tendency for a moderately skewed distribution — it expresses Mode in terms of Mean and Median with specific integer coefficients.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)