Given a histogram displayed on a graphing calculator that shows most data values clustered to the left with a long tail extending to the right, which of the following best describes the distribution of the data?

• A. The distribution is left-skewed ($\text{negatively skewed}$).
• B. The distribution is $\text{uniform}$.
• C. The distribution is right-skewed ($\text{positively skewed}$).
• D. The distribution is $\text{symmetric}$.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the shape of the distribution by analyzing the histogram. When most data values are clustered on the left side and there is a long tail extending to the right, this indicates an asymmetry in the data.
2. Step 2: Recall the definitions of skewness: a distribution is right-skewed (positively skewed) if the tail on the right side is longer or fatter than the left side, and left-skewed (negatively skewed) if the tail on the left side is longer.
3. Step 3: Compare the given histogram description to these definitions. Since the tail extends to the right, the distribution has a longer right tail, which matches the characteristics of a right-skewed distribution.
4. Step 4: Eliminate other options: a uniform distribution has roughly equal frequencies across all bins, a symmetric distribution has balanced tails on both sides, and a left-skewed distribution has a long tail on the left side, none of which match the given histogram.
5. Step 5: Conclude that the best description of the distribution is right-skewed (positively skewed) based on the clustering of data on the left and the long tail on the right.