Given the following frequency histogram that displays the final grades of a random sample of college students, which of the following statements is most likely true about the distribution of the grades?

• A. The distribution is approximately symmetric, with most students scoring near the middle grade range.
• B. The distribution is bimodal, with two distinct peaks in the grade frequencies.
• C. The distribution is skewed to the right, indicating that most students received lower grades and fewer received higher grades.
• D. The distribution is skewed to the left, indicating that most students received higher grades and fewer received lower grades.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the key terms related to distribution shapes. A distribution is symmetric if it looks roughly the same on both sides of the center. It is bimodal if there are two distinct peaks or modes. Skewness refers to the direction in which the tail of the distribution extends: skewed right means a longer tail on the right (higher values), skewed left means a longer tail on the left (lower values).
2. Step 2: Analyze the frequency histogram by observing where the majority of the data points (grades) are concentrated. If most students have higher grades and fewer have lower grades, the bulk of the data will be on the right side of the histogram, with a tail extending to the left.
3. Step 3: Identify the shape of the distribution based on the histogram. If the tail extends to the left and the peak is towards the higher grades, this indicates a left-skewed distribution.
4. Step 4: Compare the options given with your observations. Since the histogram shows most students scoring higher grades and fewer scoring lower grades, the distribution is skewed to the left.
5. Step 5: Conclude that the correct statement is the one describing a left-skewed distribution, meaning most students received higher grades and fewer received lower grades.