Which of the following distributions is left skewed when displayed on a graphing calculator?

• A. A distribution where most data values are clustered on the $\mathrm{right}$ and the tail extends to the $\mathrm{left}$
• B. A distribution where most data values are clustered on the $\mathrm{left}$ and the tail extends to the $\mathrm{right}$
• C. A distribution that is $\mathrm{symmetric}$ with equal tails on both sides
• D. A distribution with $2$ distinct peaks of equal height

Answer: (A)

Verified step by step guidance

1. Understand the concept of skewness in a distribution: skewness refers to the asymmetry in the shape of the distribution's graph.
2. Recall that a left-skewed distribution (also called negatively skewed) has a longer tail on the left side, meaning the bulk of the data is concentrated on the right.
3. Identify that in a left-skewed distribution, the tail extends towards the smaller values (left side), while most data values cluster on the right side of the graph.
4. Compare this to other options: a right-skewed distribution has the tail on the right, a symmetric distribution has equal tails on both sides, and a distribution with two peaks is bimodal, not skewed.
5. Conclude that the correct description of a left-skewed distribution is one where most data values are clustered on the right and the tail extends to the left.