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 not correct in perfectly symmetrical distributions. In fact, the distance from Q₁ to Q₃ is equal to the distance from the median to the minimum value, or the distance from the median to the maximum value. Therefore, it is not necessarily half of the distance from the smallest to the largest observation. Statements A, B, and C are correct in perfectly symmetrical distributions, as the quartiles divide the distribution into four equal parts.

In Perfectly Symmetrical Distributions, Which of the Following Is Not