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 ______________.

Verified step by step guidance

1. Understand the components of a boxplot: the box represents the interquartile range (IQR), the line inside the box is the median, and the whiskers extend to the smallest and largest data points within 1.5 times the IQR from the quartiles.
2. Note that if the median is to the left of the center of the box, it means the median is closer to the first quartile (Q1) than to the third quartile (Q3). This suggests that the lower half of the data is more tightly packed than the upper half.
3. Observe that the right whisker being substantially longer than the left whisker indicates that there is a longer spread or more extreme values on the higher end of the data.
4. Combine these observations: a median closer to the lower quartile and a longer right whisker typically indicate that the distribution has a longer tail on the right side.
5. Conclude that the distribution is skewed to the right (positively skewed) because the tail on the right side is longer and the bulk of the data is concentrated on the left.

Key Concepts

Boxplot Components

A boxplot visually summarizes data using five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box represents the interquartile range (IQR) between Q1 and Q3, with a line inside indicating the median. Whiskers extend from the box to the smallest and largest data points within 1.5 times the IQR.

Skewness in Distributions

Skewness describes the asymmetry of a data distribution. A distribution is right-skewed (positively skewed) if the tail on the right side is longer or fatter, and left-skewed (negatively skewed) if the left tail is longer. Skewness affects the position of the median relative to the quartiles and the length of whiskers in a boxplot.

Interpreting Median and Whiskers in Boxplots

In a boxplot, if the median is closer to the left side of the box and the right whisker is longer, it indicates more spread or extreme values on the right side. This pattern suggests a right-skewed distribution, where the bulk of data is concentrated on the lower end with a tail extending to higher values.