Question 1: Calculate the median and interquartile range (IQR) of the data set: 3, 7, 8, 5, 10, 12, 6.

Answer: {"IQR":5,"median":7}

Question 2: Construct a box plot for the following data: 4, 9, 5, 7, 10, 6, 8.

Answer: Student draws box plot on grid

Question 3: Compare the two box plots: Data Set A (1, 3, 4, 6, 8, 10) and Data Set B (2, 4, 5, 7, 9, 11). Which distribution has a larger spread?

Answer: Data Set B

Question 4: A box plot shows a median of 15, with Q1 at 10 and Q3 at 20. What is the IQR?

Answer: See full answer key

Question 5: A data set has a median of 25, with the lower quartile at 20 and the upper quartile at 30. If the minimum value is 15 and the maximum is 35, draw an appropriate box plot on the grid.

Answer: Student draws box plot with min 15, Q1 20, median 25, Q3 30, max 35

Question 6: A box plot of students' test scores shows a median of 78, Q1 at 70, Q3 at 85, with an outlier at 55. Explain what this outlier indicates about the data.

Answer: The outlier indicates a student scored much lower than others, possibly an unusual or exceptional case.

Question 7: Identify the common mistake: A student calculates the IQR by subtracting the minimum from Q3. Correct the mistake.

Answer: IQR = Q3 - Q1, not min - Q3

Question 8: Given the box plot data: Min = 12, Q1=20, Median=25, Q3=30, Max=40, identify the range and interpret it.

Answer: Range = 40 - 12 = 28; it shows the total spread of the data.

Question 9: The box plot for Class A shows a median of 75 and for Class B a median of 85. Which class performed better generally?

Answer: Class B

Question 10: Challenge: If a new data set has a median of 50, Q1 of 45, and Q3 of 55, with a maximum of 70, what is the possible minimum value if the data is normally distributed?

Answer: Approximately 30-35 (student draws and explains reasoning)

Question 11: Error Analysis: A student reports the IQR as Q3 minus the minimum value. Why is this incorrect and what should they do instead?

Answer: They should subtract Q1 from Q3 to find the IQR, not subtract the minimum.