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: Use the mean-mode gap version of the empirical relation.
The same relation can be written as $\text{Mean}-\text{Mode}=3(\text{Mean}-\text{Median})$.
Step 2: Plug in the known values.
Mean $=43$, Median $=40$, so Mean $-$ Median $=3$, giving Mean $-$ Mode $=3\times3=9$.
Step 3: Solve for the Mode.
$43-\text{Mode}=9 \implies \text{Mode}=34$, matching option (A).
\[ \boxed{34} \]