Step 1: Understanding the Concept:
Mean, Median, and Mode are the three primary measures used to describe the center of a data distribution.
In a perfectly symmetrical distribution, all three values are identical.
However, most real-world data is skewed (asymmetrical).
For moderately skewed distributions, mathematicians have established an "Empirical Relationship" that links these three measures.
This formula is extremely useful when the raw data points are missing but two of the descriptive statistics are known.
Step 2: Key Formula or Approach:
The empirical relationship is defined as:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 3: Detailed Explanation:
From the problem description, we identify the given parameters:
Median = 12
Mean = 15
We need to solve for the Mode. Using the formula:
\[ \text{Mode} = 3(12) - 2(15) \]
First, calculate the product of 3 and the median:
\[ 3 \times 12 = 36 \]
Next, calculate the product of 2 and the mean:
\[ 2 \times 15 = 30 \]
Finally, subtract the second result from the first:
\[ \text{Mode} = 36 - 30 = 6 \]
The mode of this specific frequency distribution is 6.
Step 4: Final Answer:
The mode of the given frequency distribution is 6.