Question

Match List-I with List-II \[\begin{array}{|c|c|} \hline \textbf{Nature of Skewness for a Distribution} & \textbf{Relationship between Arithmetic Mean (AM), Median and Mode} \\ \hline \text{(A) Positively Skewed} & \text{(I) AM = Median = Mode} \\ \hline \text{(B) Moderately Skewed} & \text{(II) AM < Median < Mode} \\ \hline \text{(C) Negatively Skewed} & \text{(III) AM - Mode = 3 (AM - Median)} \\ \hline \text{(D) Symmetric Distribution} & \text{(IV) AM > Median > Mode} \\ \hline \end{array}\] Choose the correct answer from the options given below:

• (A) - (II), (B) - (I), (C) - (III), (D) - (I)
• (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
• (A) - (I), (B) - (II), (C) - (IV), (D) - (III)
• (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Hint:

For skewed distributions: in a positively skewed distribution, AM > Median > Mode, and in a negatively skewed distribution, Mode > Median > AM.

Answer 1

The Correct Option is D

Step 1: Understanding the relationship between AM, Median, and Mode.
- **Positively Skewed (A):** In a positively skewed distribution, the tail is stretched to the right. In this case, the mode is less than the median, and the median is less than the mean. Therefore, the correct relationship is **AM > Median > Mode**. This corresponds to **(III)** in List-II.
- **Moderately Skewed (B):** A moderately skewed distribution has a small skew. The relationship between the mean, median, and mode is typically **AM < Median < Mode**. This corresponds to **(IV)** in List-II.
- **Negatively Skewed (C):** In a negatively skewed distribution, the tail is stretched to the left. The relationship is given by **AM - Mode = 3 (AM - Median)**. This corresponds to **(II)** in List-II.
- **Symmetric Distribution (D):** In a symmetric distribution, the mean, median, and mode are all equal. This corresponds to **(I)** in List-II.

Step 2: Conclusion.
The correct answer is **(A) - (III), (B) - (IV), (C) - (II), (D) - (I)**.