Problem:
Given:
- Mean = 21
- Median = 23
Find the mode.
Step 1: Apply the empirical relationship for skewed distributions
The empirical formula connecting mean, median, and mode for moderately skewed data is:
\[
\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}
\]
Step 2: Calculate the mode
Substitute the given values:
\[
\text{Mode} = 3 \times 23 - 2 \times 21 = 69 - 42 = 27
\]