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 formula is to connect the larger coefficient with the longer word:
"Median" has 6 letters and gets multiplied by 3.
"Mean" has 4 letters and gets multiplied by 2.
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This prevents you from swapping the coefficients during exams!

Answer 1

The Correct Option is A

Step 1: Rearrange the empirical formula.
Starting from $\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}$, we can regroup it as:
\[ \text{Mode} = \text{Median} + 2(\text{Median} - \text{Mean}) \]
Step 2: Find the difference between median and mean.
\[ \text{Median} - \text{Mean} = 40 - 43 = -3 \]
Step 3: Substitute back to find the mode.
\[ \text{Mode} = 40 + 2(-3) = 40 - 6 = 34 \]
\[ \boxed{\text{Mode} = 34} \]