Let M. Md, Mo, Q1 and Q3 denote the mean, median, mode, and first and third quartile of distribution, respectively. Which of the following is correct for positively skewed distribution?

Question

Question

This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

The correct answer is Q1 + Q3 > 2 Md

Key Points

In a positively skewed distribution, the tail of the distribution extends towards the right side, indicating that there are relatively more extreme values on the right side of the distribution. As a result, the median (Md) tends to be smaller than the mean (M) in such distributions.
When examining quartiles, the first quartile (Q1) represents the value below which approximately 25% of the data lies, and the third quartile (Q3) represents the value below which approximately 75% of the data lies. Since the distribution is positively skewed, Q3 tends to be farther away from the median (Md) compared to Q1.
Therefore, in a positively skewed distribution, it holds true that Q1 + Q3 is greater than 2 times the median (Q1 + Q3 > 2Md). This inequality is a consequence of the long tail on the right side, resulting in a larger spread in the upper half of the distribution relative to the lower half.