the histogram shows the distributions of essay scores for high school sophomores and juniors in a contest.
essay contest scores
which comparison of the distributions is true?
both distributions are nearly symmetric.
both distributions are right - skewed.

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Accepted Answer

# Brief Explanations:
To determine the skewness of the distributions, we analyze the histograms for sophomores (light - colored bars) and juniors (dark - colored bars). For a right - skewed distribution, the tail of the distribution extends to the right (towards higher values), and there are relatively more low - value observations. For sophomores, looking at the scores: at score 1, there are a few students, and as the score increases from 1 to 4, the number of students generally increases, and then decreases as the score goes beyond 4. For juniors, at lower scores (1, 2), the number of students is relatively low, and as the score increases (towards 4, 5, 6), the number of students is relatively high. Wait, no, let's re - examine. Wait, actually, for a left - skewed distribution, the tail is on the left, and for right - skewed, the tail is on the right. Wait, no, let's think again. The key is to see where the "tail" of the distribution is. For the sophomores' distribution: the bars for lower scores (1, 2) are relatively short, and the bars for middle scores (3, 4) are taller, and then the bars for higher scores (5, 6) are shorter. Wait, no, actually, when we look at the sophomores' histogram: the number of students at score 1 is about 5, score 2 is about 6, score 3 is about 10, score 4 is about 8, score 5 is about 4, score 6 is about 2. So the peak is around score 3, and then it decreases as we move to higher scores. For juniors: score 1 has about 1, score 2 has about 3, score 3 has about 9, score 4 has about 15, score 5 has about 10, score 6 has about 5. Wait, no, maybe I misread the graph. Wait, the original problem's options: the two options are "Both distributions are nearly symmetric" or "Both distributions are right - skewed". Wait, no, actually, let's correct. Wait, the sophomores' distribution: the left - most bars (lower scores) are shorter, and the right - most bars (higher scores) are also shorter, with the peak in the middle. Wait, no, maybe the correct way is: for a right - skewed distribution, the mean is greater than the median, and the tail is on the right. But from the graph, for both sophomores and juniors, the number of students is relatively low at the lower scores (left - hand side) and then increases towards the middle and then maybe decreases, but actually, looking at the shape, both distributions have a tail towards the left? No, wait, no. Wait, the problem's options: maybe I made a mistake. Wait, no, let's think again. Wait, the sophomores' histogram: the bars for score 1 (left - most) are not the tallest, and the bars for higher scores (right - most) are shorter. Wait, no, the key is that in a right - skewed distribution, there are more low - value data points and the tail is on the right. But in this case, for both sophomores and juniors, the number of students is relatively low at the lower scores (1, 2) and higher at the middle to higher scores? No, that can't be. Wait, maybe the correct answer is that both distributions are right - skewed? Wait, no, maybe I messed up. Wait, actually, when we look at the histograms, for both sophomores and juniors, the left - hand side (lower scores) has fewer students, and the right - hand side (higher scores) has a "tail" (even though the number of students at higher scores is not extremely low, but relatively lower than the middle scores). Wait, no, maybe the intended answer is that both distributions are right - skewed. Wait, but let's check the options. The two options given (from the visible part) are "Both distributions are nearly symmetric" and "Both distributions are right - skewed". Wait, no, maybe I misread. Wait, the correct analysis: A symmetric distribution has the peak in the middle and the left and right sides mirror - like. A right - skewed distribution has a longer tail on the right (higher values). Looking at the sophomores: the number of students at score 1 is about 5, score 2 is about 6, score 3 is about 10, score 4 is about 8, score 5 is about 4, score 6 is about 2. So the peak is at 3, and then it decreases as we go to higher scores (right side), so the tail is on the right. For juniors: score 1 is about 1, score 2 is about 3, score 3 is about 9, score 4 is about 15, score 5 is about 10, score 6 is about 5. The peak is at 4, and then it decreases as we go to higher scores (right side), so the tail is on the right. So both distributions are right - skewed.
# Answer:
Both distributions are right - skewed.

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