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?
section minimum q1 median q3 maximum
morning 59 64.5 72 90 100
evening 18 31.5 72 85.5 93
none of the other answer options are correct.
test scores are less variable in the evening section compared to the morning section.
test scores in the morning section are skewed to the left.
when compared to the morning section, a larger percentage of students in the evening section had scores below 72.
there are fewer students in the morning section compared to the evening section.

Explanation:

Step1: Analyze range for variability

Range = Maximum - Minimum. For morning: $100 - 59=41$. For evening: $93 - 18 = 75$. So evening has more variability, ruling out the option about less variability in evening.

Step2: Check skewness for morning

In the morning section, $Q_1 = 64.5$, Median = 72, $Q_3=90$. Since $Q_3 - Median=90 - 72 = 18$ and $Median - Q_1=72 - 64.5 = 7.5$, and $Q_3 - Median>Median - Q_1$, the morning - section is skewed to the right, not left.

Step3: Analyze median comparison

The median for both sections is 72. In the evening section, 50% of students have scores below the median (72). In the morning section, 50% of students have scores below the median (72). But the spread of scores below the median in the evening section is much wider due to the lower minimum and $Q_1$. So a large percentage of students in the evening section had scores below 72 compared to the morning section.

Step4: No information about number of students

There is no information in the box - plots or summary statistics about the number of students in each section.

Answer:

When compared to the morning section, a large percentage of students in the evening section had scores below 72.