Which of the following histograms best depicts a moderately left-skewed distribution?

• A. A histogram that is symmetric with data evenly distributed around the center.
• B. A histogram where most of the data are concentrated on the right with a longer tail extending to the left.
• C. A histogram where most of the data are concentrated on the left with a longer tail extending to the right.
• D. A histogram with two distinct peaks of similar height.

Answer: (B)

Verified step by step guidance

1. Understand the concept of skewness in a distribution: skewness refers to the asymmetry in the shape of the data distribution. A left-skewed (or negatively skewed) distribution has a longer tail on the left side.
2. Identify the characteristics of a left-skewed distribution in a histogram: most data values are concentrated on the right side, and the tail extends towards the left.
3. Compare the given options with the characteristics of a left-skewed distribution: a symmetric histogram is not skewed, a histogram with a longer tail on the right is right-skewed, and a histogram with two peaks is bimodal, not skewed.
4. Recognize that the correct histogram for a moderately left-skewed distribution is the one where most data are concentrated on the right with a longer tail extending to the left.
5. Summarize that the key visual cue for left skewness is the tail direction (left) and the concentration of data on the opposite side (right).