If Q₁, Q₂, and Q₃ are three quartiles of a frequency distribution, which of…
2021
If Q₁, Q₂, and Q₃ are three quartiles of a frequency distribution, which of the following holds if the distribution is negatively skewed?
- A.
Q₁ + Q₃ > 2Q₂
- B.
Q₁ + Q₃ < 2Q₂
- C.
Q₁ + Q₂ < 2Q₃
- D.
Q₃ − Q₁ > 2Q₂
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Correct answer: B
In a negatively skewed distribution, the data is concentrated on the right with a longer tail extending to the left. This implies that the distance between the first quartile (Q₁) and the median (Q₂) is greater than the distance between the median and the third quartile (Q₃). Consequently, Q₁ + Q₃ < 2Q₂.