Question

If the mean and mode of a data are 12 and 21 respectively, then its median is :

• A. 6
• B. 13.5
• C. 15
• D. 14

Hint:

A simple way to remember the formula is to arrange the terms alphabetically: Mean, Median, Mode.
The formula uses the coefficients 3 and 2. The larger coefficient (3) goes with the word having more letters (Median), and the smaller coefficient (2) goes with the word having fewer letters (Mean).
Formula: \(\text{Mode} = 3(\text{Median}) - 2(\text{Mean})\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In statistics, there is an empirical relationship that connects the three measures of central tendency: Mean, Median, and Mode.
This relationship is particularly useful for moderately skewed distributions where you are given two values and need to find the third.
Step 2: Key Formula or Approach:
The empirical formula is given by:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 3: Detailed Explanation:
Given:
Mean = 12
Mode = 21
Let the Median be \(M\).
Substituting the values into the formula:
\[ 21 = 3 \times M - 2 \times 12 \]
\[ 21 = 3M - 24 \]
Add 24 to both sides:
\[ 21 + 24 = 3M \]
\[ 45 = 3M \]
Divide by 3:
\[ M = \frac{45}{3} \]
\[ M = 15 \]
Step 4: Final Answer:
The median of the data is 15.