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: Analyzing the relationship between Mean (AM), Median, and Mode.

- Positively Skewed (A): In a positively skewed distribution, the tail extends to the right. The order is Mode < Median < Mean. This matches (III).

- Moderately Skewed (B): A moderately skewed distribution exhibits a slight skew. The typical relationship is Mean < Median < Mode. This matches (IV).

- Negatively Skewed (C): In a negatively skewed distribution, the tail extends to the left. The relationship is described by AM - Mode = 3 (AM - Median). This matches (II).

- Symmetric Distribution (D): In a symmetric distribution, Mean = Median = Mode. This matches (I).

Step 2: Final Answer.

The correct pairings are: (A) - (III), (B) - (IV), (C) - (II), (D) - (I).