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 the "3-2-1" rule: 3 Median - 2 Mean = 1 Mode.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For any distribution, there is an empirical relationship between the three measures of central tendency: Mean, Median, and Mode.
Step 2: Key Formula or Approach:
\[ \text{Mode} = 3(\text{Median}) - 2(\text{Mean}) \]
Step 3: Detailed Explanation:
1. Given: Mean = 12, Mode = 21. 2. Substitute the values into the empirical formula: \[ 21 = 3(\text{Median}) - 2(12) \] 3. Solve for Median: \[ 21 = 3(\text{Median}) - 24 \] \[ 21 + 24 = 3(\text{Median}) \] \[ 45 = 3(\text{Median}) \] \[ \text{Median} = \frac{45}{3} = 15 \]
Step 4: Final Answer:
The median of the data is 15.