Questions: In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed

Solution Steps

A boxplot consists of a box and whiskers. The box represents the interquartile range (IQR), which is the range between the first quartile (\( Q_1 \)) and the third quartile (\( Q_3 \)). The median (\( Q_2 \)) is represented by a line inside the box. The whiskers extend to the minimum and maximum values within 1.5 times the IQR from the quartiles.

If the median is to the left of the center of the box, it indicates that the data is not symmetrically distributed. Specifically, more data points are concentrated on the right side of the median, suggesting a longer tail on the right.

A substantially longer right whisker compared to the left whisker further supports the idea of a longer tail on the right side of the distribution. This asymmetry indicates that the distribution is skewed to the right (positively skewed).

Final Answer