During a recent semester at University X, 25 students enrolled in an economics class. Each student was enrolled in the...

OWNING THE DATASET

Let's start by understanding what we're working with. This table contains information about 25 students with their exam scores and final grades. For each student, we have:

• Name
• Year in program (1, 2, or 3)
• Exam 1 score
• Exam 2 score
• Final exam score
• Final score (a weighted combination of the three exams)

For example, looking at one row: Radzinsky is in year 3, scored 91 on Exam 1, 95 on Exam 2, 100 on the Final exam, and received a final score of 96.5.

Key insight: The final score appears to be calculated using weighted values from the three exams. Understanding these weights will be crucial for evaluating Statement 1.

Instead of manually scanning this large dataset, we'll leverage sorting techniques to quickly reveal patterns and answer our questions efficiently.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "The median final score for all 25 students was 81.50"
What we're looking for:

• The middle value (13th position) when all 25 final scores are arranged in order
• Whether this middle value equals 81.50

In other words: Is the median final score exactly 81.50?

Let's tackle this statement first because sorting makes finding a median incredibly efficient.

Approach: We'll sort the entire table by the "Final score" column in ascending order. With 25 students, the median will be the 13th value.

1. Let's sort by "Final score" (ascending)
2. After sorting, we can immediately identify the 13th student (middle of 25)
3. Looking at the 13th row, we see the student Orlando has a final score of 81.50

Teaching callout: Notice how sorting eliminated the need to manually arrange all 25 scores or count values. The sort function does all that work instantly, placing the median value exactly where we need it.

Conclusion for Statement 2: Yes ✓

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "For Exam 1 scores for students in year 3 of the program, the range was 40"
What we're looking for:

• All students who are in year 3 of the program
• The highest and lowest Exam 1 scores among these year 3 students
• Whether the difference (range) between highest and lowest equals 40

In other words: Is the difference between the highest and lowest Exam 1 scores for year 3 students exactly 40 points?

This statement requires us to work with a subset of students. Sorting will again be our powerful ally.

Approach: We'll use a double-sort strategy to isolate year 3 students and find their score range.

1. First, let's sort by "Year in program" to group all year 3 students together
2. Now we can easily see that there are 6 students in year 3
3. Next, while focusing only on these 6 students, let's sort by "Exam 1 score"
4. After sorting, we can immediately see:
   • Lowest Exam 1 score for year 3: Sykes with 51
   • Highest Exam 1 score for year 3: Radzinsky with 91
5. Calculate the range: \(91 - 51 = 40\)

Teaching callout: The double-sort approach saves tremendous time compared to manually finding all year 3 students and then scanning their scores. Sorting creates visual groupings that make extremes obvious.

Conclusion for Statement 3: Yes ✓

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "The score on the final exam had equal weight with the score on Exam 2 in computing the final score"
What we're looking for:

• The weighting formula used to calculate the final score
• Whether Exam 2 and Final exam have equal influence on the final score

In other words: Do Exam 2 and Final exam contribute equally to the calculated final score?

This statement requires understanding the relationship between the exam scores and the final score. Instead of setting up complex algebra, we can use strategic sampling.

Approach: Let's find students with a notable difference between their Exam 2 and Final exam scores, then see which score the final score favors.

1. Looking at Radzinsky's scores:
   • Exam 1: 91
   • Exam 2: 95
   • Final exam: 100
   • Final score: 96.5
2. If Exam 2 and Final exam had equal weights, the final score would be equally influenced by both. But we see the final score (96.5) is much closer to the Final exam score (100) than to the Exam 2 score (95).
3. Let's verify with another example. Looking at Benson:
   • Exam 2: 80
   • Final exam: 75
   • Final score: 76.75
   Again, the final score is closer to the Final exam than to Exam 2.
4. This pattern shows that the Final exam has more influence than Exam 2 in calculating the final score, meaning they do not have equal weight.

Teaching callout: Strategic sampling with just 1-2 well-chosen examples can reveal patterns without complex calculations. By selecting students with divergent Exam 2 and Final exam scores, we could clearly see which exam had more influence.

Conclusion for Statement 1: No ✗

FINAL ANSWER COMPILATION

After analyzing all three statements:

• Statement 1: No ✗ (Final exam and Exam 2 do not have equal weights)
• Statement 2: Yes ✓ (The median final score is 81.50)
• Statement 3: Yes ✓ (The range of Exam 1 scores for year 3 students is 40)

Our answer is therefore: No Yes Yes

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: We used sorting as our primary tool to quickly reveal patterns and find values like medians and ranges
• Targeted Sampling: Instead of complex algebra, we used strategic examples to test relationships
• Pattern Recognition: We identified trends in how final scores relate to exam scores without exhaustive calculations

Strategic Insights

1. Tackle statement order strategically: We started with Statement 2 because sorting immediately reveals medians, then moved to Statement 3 (another sorting-friendly question), and left the more complex Statement 1 for last.
2. Sort first, calculate later: Sorting is incredibly powerful for finding medians, ranges, and other statistical measures. It transforms a messy dataset into an organized structure where patterns become obvious.
3. Double-sort technique: When working with subsets of data (like year 3 students), sorting by one criterion and then another isolates exactly what you need.
4. Strategic examples beat algebraic systems: For complex relationships, finding one or two examples with divergent values can quickly reveal patterns without setting up and solving equations.

Common Mistakes We Avoided

• Manually arranging 25 scores to find the median
• Checking each student one by one to identify all year 3 students
• Creating a complex system of equations to determine weights
• Performing unnecessary calculations on all 25 students

Remember: In table analysis questions, sorting is often your most powerful first move. It transforms messy data into organized information where patterns and relationships become immediately visible!