If the distribution of a data set were perfectly symmetrical, the distance from Q₁ to the median would always equal the distance from Q₃ to the median in a boxplot.

Question

Quizplus · Accepted Answer

This statement is true for a perfectly symmetrical distribution. In a symmetrical distribution, the median is the same as the mean, and the interquartile range (IQR) is the same on both sides of the median. Therefore, the distance from Q₁ to the median is the same as the distance from Q₃ to the median in a boxplot for a symmetrical distribution. This is true because the first quartile(Q₁) and third quartile(Q₃) divide the data into four equal parts and the median divides the data into two equal parts. If the distribution is perfectly symmetrical, the distances from the median to Q₁ and Q₃ would be equal, resulting in an equal distance from Q₁ to the median and Q₃ to the median.

If the Distribution of a Data Set Were Perfectly Symmetrical