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:

An easy way to memorize this empirical formula is to associate the larger multiplier with the longer word:
- The word "Median" has 6 letters, so its multiplier is 3.
- The word "Mean" has 4 letters, so its multiplier is 2.
Thus:
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This mnemonic ensures you never mix up the coefficients during an exam!

Answer 1

The Correct Option is A

Step 1: Recall the alternate form of the empirical formula.
The usual empirical relation \(\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}\) can be rearranged as: \[ \text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median}) \]
Step 2: Substitute the given values into this form.
\[ \text{Mean} - \text{Mode} = 3(43 - 40) = 3 \times 3 = 9 \]
Step 3: Solve for the Mode.
\[ \text{Mode} = \text{Mean} - 9 = 43 - 9 = 34 \]
Step 4: State the final answer.
The Mode is 34, matching option (A).
\[ \boxed{\text{Mode} = 34} \]