Based on the histograms, which of the following statements is most likely true about the distribution of the data?

• A. The data are left-skewed, with a longer tail on the left side.
• B. The data are approximately symmetric with no apparent skewness.
• C. The data are right-skewed, with a longer tail on the right side.
• D. The data are uniformly distributed across all intervals.

Answer: (C)

Verified step by step guidance

1. Understand the concept of skewness: Skewness describes the asymmetry of a distribution. A right-skewed distribution has a longer tail on the right side, while a left-skewed distribution has a longer tail on the left side. A symmetric distribution has roughly equal tails on both sides.
2. Examine the histogram carefully: Look at the shape of the bars. If the bars gradually decrease in height towards the right, it suggests a right-skewed distribution. If they decrease towards the left, it suggests left-skewness. If the bars are roughly the same height on both sides, the distribution is symmetric.
3. Identify the tail: The 'tail' refers to the part of the distribution where the frequencies taper off. For right-skewness, the tail extends to the right (higher values). For left-skewness, the tail extends to the left (lower values).
4. Compare the options given: Since the correct answer states the data are right-skewed, confirm that the histogram shows a longer tail on the right side, meaning more spread or outliers on the higher value end.
5. Rule out other options: Uniform distribution would show bars of roughly equal height across intervals, and symmetric distribution would have balanced tails. Confirm these do not match the histogram's shape.