Question

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

• A. \(34\)
• B. \(43\)
• C. \(38.5\)
• D. \(41.5\)

Hint:

A simple mnemonic to remember this is "3 Medians minus 2 Means equals 1 Mode". Note the alphabetical order: Median comes before Mean if you reverse the order of subtrahends.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
There is an empirical relationship between mean, median, and mode for a moderately skewed distribution.
Step 2: Key Formula or Approach:
Empirical formula: \(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\).
Step 3: Detailed Explanation:
Given: \(\text{Mean} = 43\), \(\text{Median} = 40\).
Substitute these into the formula:
\[ \text{Mode} = 3(40) - 2(43) \]
\[ \text{Mode} = 120 - 86 \]
\[ \text{Mode} = 34 \]
Step 4: Final Answer:
The value of the mode is \(34\).