In perfectly symmetrical distributions, which of the following is NOT a correct statement?
A)The distance from Q₁ to Q₂ equals to the distance from Q₂ to Q₃.
B)The distance from the smallest observation to Q₁ is the same as the distance from Q₃ to the largest observation.
C)The distance from the smallest observation to Q₂ is the same as the distance from Q₂ to the largest observation.
D)The distance from Q₁ to Q₃ is half of the distance from the smallest to the largest observation.

Question

Quizplus · Accepted Answer

This statement is incorrect in perfectly symmetrical distributions. The distance from Q₁ to Q₃ is actually equal to the distance from the smallest observation to Q₁ and also equal to the distance from Q₃ to the largest observation. Therefore, statement D is not correct. Statements A, B, and C are all correct in perfectly symmetrical distributions. In perfectly symmetrical distributions, the distance from Q₁ to Q₃ is equal to the distance from Q₂ to the smallest or largest observation. Therefore, option D is not a correct statement as the distance from Q₁ to Q₃ is not necessarily half of the distance from the smallest to the largest observation.

In Perfectly Symmetrical Distributions, Which of the Following Is NOT