Question

here are the distributions of quiz scores for two classes. each class has 25 students. the median for each class is 5. which histogram has the smallest iqr? histogram image of class a and class b scores vs frequency options: o class a, because it has the larger portion of its values near the median. o class b, because there is less variability in the exam scores. o class a, because it is a fairly symmetric distribution. o class b, because the range is smaller.

Explanation:

To determine which histogram has the smallest IQR, we analyze the variability of the data. IQR (Interquartile Range) measures the spread of the middle 50% of data. A distribution with values more concentrated near the median has less variability and thus a smaller IQR. Class A has a larger portion of its values near the median (as seen from the histogram's shape, with more frequency concentrated around the middle scores), indicating less spread in the middle 50% of data, leading to a smaller IQR. Other options: Symmetry doesn't directly relate to IQR size, less variability in Class B is incorrect (Class B's data seems more spread out), and range is not the same as IQR.

Answer:

A. Class A, because it has the larger portion of its values near the median.