Final answer:
The show_grade(score) function classifies a numerical score into letter grades based on predefined ranges. The provided statistics and stem-and-leaf plots are helpful in understanding score distributions, with indications such as the 90th percentile providing benchmarks for assessing student performance.
Step-by-step explanation:
The function show_grade(score) is meant to categorize a numerical score into a grade message. To do that, it needs a series of conditional checks to determine which grade range the score falls into and then display the appropriate message. However, the question does not specify what the messages are for each grade range, so we'll assume a standard grading scale where 90-100 is an A, 80-89 is a B, 70-79 is a C, 60-69 is a D, and below 60 is an F. Below is a simple example of how this function would look:
def show_grade(score):
if score <=100 and score >=90:
print('A')
elif score <90 and score >=80:
print('B')
elif score <80 and score >=70:
print('C')
elif score <70 and score >=60:
print('D')
else:
print('F')
This function is useful for students and educators to quickly determine the letter grade associated with a numerical score. Looking at the data provided, the stem-and-leaf plot and the histograms can help us understand the distribution of scores. The 90th percentile which is 69.4, indicates that 90 percent of the test scores fall at or below 69.4, which suggests that most students will get a D or better. The given predictive equation indicates that a student who scores 73 on a third exam can expect to get close to 179.08 on the final exam.