Subtopic: Mean, median, mode and standard deviation
Question Statement:
For a moderately skewed frequency distribution, Karl Pearson's empirical relationship is $\text{Mode} \approx 3\text{Median} - 2\text{Mean}$. If the Mean is $32$ and the Median is $35$, the empirical Mode is ________ (answer in integer).
Answer Key:
41
Step-by-Step Solution & Explanation
Using Karl Pearson's empirical formula relating measures of central tendency:
$\text{Mode} = 3\text{Median} - 2\text{Mean}$
Substitute the given values:
$\text{Mode} = 3(35) - 2(32) = 105 - 64 = 41$