Question

midterm exam scores from students in a morning and an evening section of an anatomy course are summarized below. based on this information, what should we conclude?
test scores in the evening section are symmetric.
when compared to the evening section, a larger percentage of students in the morning section had scores below 72.
its impossible to know which section has more students enrolled in it.
none of the other answer options are correct.
test scores are more variable in the evening section compared to the morning section.

Explanation:

Step1: Analyze symmetry

For a symmetric distribution, \(Q_1 - \text{Min}\approx\text{Max}-Q_3\) and \(Q_2 - Q_1\approx Q_3 - Q_2\).
For evening section: \(Q_1 - \text{Min}=64.5 - 59 = 5.5\), \(\text{Max}-Q_3=100 - 90=10\). So evening - section scores are not symmetric.

Step2: Analyze percentage below median

Median (\(Q_2\)) represents the 50 - th percentile. Since median of both sections is 72, 50% of students in morning and 50% of students in evening have scores below 72.

Step3: Analyze variability

Inter - quartile range (\(IQR = Q_3 - Q_1\)).
For morning: \(IQR=85.5 - 31.5 = 54\).
For evening: \(IQR=90 - 64.5 = 25.5\). Morning - section scores are more variable.

Step4: Analyze number of students

Box - plots and summary statistics (min, \(Q_1\), median, \(Q_3\), max) do not give information about the number of data points (number of students).

Answer:

It's impossible to know which section has more students enrolled in it.