To solve this problem, let's calculate the mean, median, mode, range, and standard deviation for each student’s grades as presented.

Data

• Student A's grades: 78, 89, 95, 64, 98, 0, 87, 84, 76, 93, 89, 77, 61
• Student B's grades: 87, 79, 88, 91, 89, 77, 86, 93, 105, 89

Steps

1. Mean: Add all grades and divide by the number of grades.
2. Median: Arrange grades in ascending order and find the middle value. If there’s an even number of grades, average the two middle numbers.
3. Mode: Identify the grade(s) that appear most frequently.
4. Range: Subtract the smallest grade from the largest grade.
5. Standard Deviation: Calculate the square root of the average of squared deviations from the mean.

I’ll calculate these values and display the results in a table.I have calculated the mean, median, mode, range, and standard deviation for each set of grades. If you would like any further explanations or have additional questions, feel free to ask.

Here are some related questions you might consider:

1. How does the standard deviation affect the comparison of student performances?
2. Why is Student A's range much higher than Student B's, and what does this indicate?
3. What does the mode tell us about the grades of each student?
4. How can outliers affect the mean and standard deviation in this context?
5. How might these statistics influence an instructor's assessment of each student's overall performance?

Tip: The standard deviation helps us understand how spread out the grades are, giving insight into consistency in performance.