Question

If for a data, median is 5 and mode is 4, then mean is equal to :

• A. 7
• B. 11
• C. \(\frac{11}{2}\)
• D. \(\frac{14}{3}\)

Hint:

To remember the formula, think of the coefficients: 3 and 2. Since 3>2, the larger coefficient (3) goes with Median (6 letters) and the smaller (2) goes with Mean (4 letters).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a moderately skewed distribution, there is an empirical relationship between Mean, Median, and Mode.
Step 2: Key Formula or Approach:
Empirical Formula: \[ \text{Mode} = 3(\text{Median}) - 2(\text{Mean}) \]
Step 3: Detailed Explanation:
1. Given: Median = 5, Mode = 4.
2. Substitute into the formula:
\[ 4 = 3(5) - 2(\text{Mean}) \] 3. Simplify the equation:
\[ 4 = 15 - 2(\text{Mean}) \] 4. Rearrange to solve for Mean:
\[ 2(\text{Mean}) = 15 - 4 \] \[ 2(\text{Mean}) = 11 \] \[ \text{Mean} = \frac{11}{2} = 5.5 \]
Step 4: Final Answer:
The mean is \(\frac{11}{2}\).