Question

The median and mean of a frequency distribution are 12 and 15 respectively. Then the mode is:

• A. 3
• B. 4
• C. 6
• D. 33

Hint:

A quick way to memorize the empirical formula is to arrange the terms alphabetically: Mean, Median, Mode.
Note the coefficients: 3 goes with the longer word (Median has 6 letters) and 2 goes with the shorter word (Mean has 4 letters).
Formula: Mode = 3 Median - 2 Mean.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the median and the mean of a frequency distribution, which are 12 and 15, respectively.
We are asked to calculate the mode of this distribution.
Since the individual data points are not provided, we must use the empirical relationship established for moderately asymmetrical distributions.

Step 2: Key Formula or Approach:
The empirical relationship between Mean, Median, and Mode is:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

Step 3: Detailed Explanation:
$\bullet$ Identify the given values:
\(\text{Median} = 12\)
\(\text{Mean} = 15\)
$\bullet$ Substitute the values into the empirical formula:
\[ \text{Mode} = 3(12) - 2(15) \]
Calculate each term individually:
\[ 3 \times 12 = 36 \]
\[ 2 \times 15 = 30 \]
Subtract the terms:
\[ \text{Mode} = 36 - 30 \]
\[ \text{Mode} = 6 \]
Therefore, the mode of the frequency distribution is 6.

Step 4: Final Answer:
The mode of the given frequency distribution is 6.