Question

If the mean and mode of a data are 12 and 21 respectively, then its median is :

• A. 6
• B. 13.5
• C. 15
• D. 14

Hint:

An easy way to memorize this empirical relation is:
"3 Medians minus 2 Means equals 1 Mode."
Keep alphabetical order in mind: Median (longest word, multiplier 3) comes first, then Mean (shorter word, multiplier 2).

Answer 1

The Correct Option is C

Step 1: Rearrange the empirical relation for median directly.
Starting from $\text{Mode}=3\,\text{Median}-2\,\text{Mean}$, we can isolate the median right away: $\text{Median}=\dfrac{\text{Mode}+2\,\text{Mean}}{3}$.
Step 2: Plug in the given values.
With Mode $=21$ and Mean $=12$: $\text{Median}=\dfrac{21+2(12)}{3}=\dfrac{21+24}{3}$.
Step 3: Simplify.
$\text{Median}=\dfrac{45}{3}=15$.
\[ \boxed{15} \]