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:

To easily remember the empirical formula, write the terms in alphabetical order: Mean, Median, Mode.
The coefficient of Median is 3 (longer word) and Mean is 2 (shorter word):
\[ \text{Mode} = 3\ \text{Median} - 2\ \text{Mean} \]
This alphabetical-length connection serves as an excellent memory aid!

Answer 1

The Correct Option is C

Step 1: Work with the gap between median and mean first, instead of plugging straight into the formula.
The empirical relation between the three averages is $\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}$, but it helps to see this as a statement about how far apart Mode is from Median, based on how far apart Median already is from Mean.
Rewrite the relation as:
\[ \text{Mode} - \text{Median} = 2(\text{Median} - \text{Mean}) \]

Step 2: Find the gap between Median and Mean.
\[ \text{Median} - \text{Mean} = 43.4 - 43 = 0.4 \]

Step 3: Double this gap to get the gap between Mode and Median.
\[ \text{Mode} - \text{Median} = 2 \times 0.4 = 0.8 \]

Step 4: Add this gap to the Median to get the Mode.
\[ \text{Mode} = \text{Median} + 0.8 = 43.4 + 0.8 = 44.2 \]

Step 5: Final Answer.
The mode of the distribution is 44.2, so option (C) is correct. \[ \boxed{44.2} \]