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:

A simple way to remember the formula is the "3-2-1" rule: 3 Median - 2 Mean = 1 Mode.

Answer 1

The Correct Option is C

The problem asks us to find the median of a set of data given that its mean is 12 and its mode is 21. We can use the empirical relationship between mean, median, and mode to solve this problem. The empirical formula is typically given by:

\(\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})\)

Given:

• Mean = 12
• Mode = 21

We substitute these values into the formula:

\(12 - 21 = 3(12 - \text{Median})\)

This simplifies to:

\(-9 = 3 \times (12 - \text{Median})\)

Dividing both sides by 3 gives:

\(-3 = 12 - \text{Median}\)

Rearranging the equation to solve for the median, we get:

\(\text{Median} = 12 + 3 = 15\)

Thus, the median of the data is 15.

Let's evaluate the options provided:

• Option 1: 6 → Not correct
• Option 2: 13.5 → Not correct
• Option 3: 15 → Correct
• Option 4: 14 → Not correct

Therefore, the correct answer is 15. This is consistent with the formula and the given data.