Question 1: Calculate Q1, Q3, and the IQR for the data set: 3, 7, 8, 5, 12, 9, 10.

Answer: Q1=5, Q3=10, IQR=5

Question 2: Identify the mistake in this calculation: Q1=7, Q3=12, IQR=12-7=5.

Answer: Incorrect Q1; the quartiles were not correctly identified from the data set.

Question 3: Construct a data set where the IQR is 8. Then, find Q1, Q3, and verify the IQR.

Answer: Example data: 2, 4, 5, 9, 11, 13, 15; Q1=4, Q3=13, IQR=9

Question 4: A student calculates IQR as Q3 - Q2. Explain why this is incorrect and what the correct formula is.

Answer: The correct formula is IQR = Q3 - Q1; Q2 is the median, not used in the IQR calculation.

Question 5: Given the sorted data set: 2, 4, 6, 8, 10, 12, 14, find the IQR.

Answer: Q1=4, Q3=12, IQR=8

Question 6: A data set has Q1=15 and Q3=25. The student incorrectly calculates the IQR as 40. What is the mistake?

Answer: The student incorrectly added Q1 and Q3 instead of subtracting; correct IQR = Q3 - Q1 = 10.

Question 7: Plot the data points on the grid to represent a data set with an IQR of 6.

Answer: Students should draw points with Q1 and Q3 spaced 6 units apart.

Question 8: Explain why an extremely small IQR might indicate less variability in the data.

Answer: A small IQR means the middle 50% of data points are close together, indicating low variability.

Question 9: Find the error in this calculation: data set = 1, 2, 3, 4, 5, 6, 7; Q1=2, Q3=6, IQR=4. Is this correct?

Answer: Incorrect; Q1=2, Q3=6 is correct, so IQR=4; the calculation is actually correct.

Question 10: A dataset has an IQR of 10. If Q1=20, what is Q3?

Answer: Q3=30

Question 11: Describe a real-world scenario where calculating the IQR helps to understand data variability.

Answer: Example: In measuring students' test scores, the IQR shows how consistent the middle 50% of scores are.