Question

The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :

• A. \( 43.4 \)
• B. \( 42.4 \)
• C. \( 44.2 \)
• D. \( 49.3 \)

Hint:

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

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Use the empirical relationship: \( \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \).
Step 2: Detailed Explanation:
Given Mean = 43 and Median = 43.4.
\[ \text{Mode} = 3(43.4) - 2(43) \]
\[ \text{Mode} = 130.2 - 86 = 44.2 \]
Step 3: Final Answer:
The mode is 44.2.