Question

Mean, mode and variance of a given dataset are 60, 76 and 16, respectively. The value of Coefficient of Skewness of the dataset is:

• A. 1
• B. -1
• C. 4
• D. -4

Hint:

Exam Tip:
Karl Pearson's Coefficient of Skewness:
\[ \text{Skewness} = \frac{\text{Mean} - \text{Mode}}{\text{SD}} \]
• Positive: Right-skewed.
• Negative: Left-skewed.
• Zero: Symmetric.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Coefficient of Skewness (using Karl Pearson's formula) is given by: \[ \text{Skewness} = \frac{\text{Mean} - \text{Mode}}{\text{Standard Deviation}} \]

Step 2: Key Formula or Approach:
Given: Mean = 60, Mode = 76, Variance = 16.
Standard Deviation \(= \sqrt{16} = 4\).

Step 3: Detailed Explanation:
\[ \text{Skewness} = \frac{60 - 76}{4} = \frac{-16}{4} = -4 \] The negative sign indicates that the distribution is negatively skewed (left-skewed).

Step 4: Final Answer:
Therefore, option (D) is correct.