Question 1: Calculate the interquartile range (IQR) for the data set represented by the box plot. The box plot shows a lower quartile (Q1) of 12, a median (Q2) of 16, and an upper quartile (Q3) of 20.

Answer: 8

Question 2: Identify which of the following box plots represents a data set with the greatest spread: (A) Q1=5, Q3=10; (B) Q1=3, Q3=15; (C) Q1=8, Q3=12.

Answer: B

Question 3: A box plot shows a median of 14, with Q1 at 10 and Q3 at 20. The minimum is 5 and the maximum is 25. Calculate the range of the data set.

Answer: 20

Question 4: The box plot for group A has a median of 18, Q1 of 14, Q3 of 22, with a minimum of 10 and maximum of 26. Group B's box plot has a median of 16, Q1 of 12, Q3 of 20, with a minimum of 8 and maximum of 24. Which group has a more symmetrical distribution? Explain your reasoning.

Answer: Group B, because its median is closer to the center of the box and the spread above and below the median appears more balanced.

Question 5: Construct a box plot for the following data set: 4, 7, 9, 10, 12, 14, 15, 18. Show all key features (Q1, median, Q3, min, max).

Answer: Min=4, Q1=7, Median=11, Q3=15, Max=18

Question 6: A box plot shows two data sets with similar medians but different spreads. Data set X has Q1=10, Q3=20; Data set Y has Q1=12, Q3=18. Which data set has greater variability? Justify your answer.

Answer: Data set X, because its interquartile range (IQR) is 10, which is larger than Y's IQR of 6, indicating greater variability.

Question 7: The box plot for a dataset shows a median of 25, with Q1 at 20, Q3 at 30, a minimum of 15, and a maximum of 35. What is the median absolute deviation (MAD) if the median absolute deviations from the median are 4, 6, 5, 7, 3 for individual data points?

Answer: 4.0

Question 8: If a data set has a median of 50, Q1 of 45, and Q3 of 55, what is the approximate IQR? What does this suggest about the spread of the data?

Answer: 10; suggests moderate spread around the median.

Question 9: A box plot shows a median of 8, with Q1 at 5 and Q3 at 11. The minimum is 2 and the maximum is 14. A new data point of 17 is added. How does this affect the maximum and the overall distribution? Explain.

Answer: The maximum increases to 17, which may indicate a more skewed distribution or presence of an outlier, increasing overall spread.

Question 10: Identify and correct the mistake: A student calculates the IQR of a data set as Q3 - Q1 = 25 - 15 = 10, but reports the box plot's IQR as 15. What is the error?

Answer: The error is in the calculation; IQR should be 25 - 15 = 10, matching the actual data, so the student misread the box plot values.