Class P has an average of 5.40, the highest of the four classes, so it does not meet the condition of «neither better nor worse». Furthermore, its standard deviation of 2.89 is the largest of the four, meaning the scores are widely scattered away from the mean. This is the opposite of being concentrated around the mean, so its proportion of students scoring 4 to 6 points is in fact smaller.
×Incorrectイ
Class Q has an average of 4.40, the lowest of the four classes, so it is not «neither better nor worse» but rather a relatively poor-performing class. This alone rules it out. Its standard deviation of 2.07 is not the smallest either.
○ウ
正解The correct answer is ウ (Class R). Two pieces of information guide the judgment: the average score and the standard deviation. First, «performance neither better nor worse than the others» means the class whose average is neither the highest nor the lowest, in other words a middle-ranking average. In Table 2 the averages are P=5.40 (highest), Q=4.40 (lowest), R=5.00, and S=5.00, so the candidates narrow down to Class R and Class S. Next, «many students scored close to that class's average» means the data is concentrated around the mean, that is, the spread is small, which means the standard deviation is small. Class R's standard deviation of 1.02 is smaller than Class S's 2.07, and it is the smallest of the four classes. Therefore Class R, which has a middle-ranking average and the smallest spread, is the answer. In fact, for Class R the range of average 5.00 ± standard deviation 1.02 almost exactly covers 4 to 6 points, so the proportion of students scoring 4 to 6 points is the highest.
×Incorrectエ
Class S has an average of 5.00, a middle-ranking average just like Class R, but its standard deviation is 2.07, about twice Class R's 1.02. In other words, even with the same average, its scores are spread more widely away from the mean, so it cannot be said that «many students scored close to the average». When the averages are the same, the smaller standard deviation indicates greater concentration around the mean, so Class R is chosen.
ここがポイント
The mean (average score) shows where the center of the data lies, while the standard deviation shows how large the spread (dispersion) of the data is. The smaller the standard deviation, the more the data clusters near the mean.
When comparing groups with the same mean, use the standard deviation to decide. Since most data falls within the range of mean ± standard deviation, the class with the smallest standard deviation has the highest proportion of scores near the mean (here, 4 to 6 points).