Question 1: Calculate the interquartile range (IQR) for the data set: 3, 7, 8, 5, 9, 2, 6, 4.

Answer: 4

Question 2: Identify the median of the following box plot data: Minimum = 2, Q1 = 4, Median = 6, Q3 = 8, Maximum = 10.

Answer: 6

Question 3: Construct a box plot for the data: 12, 15, 14, 10, 13, 16, 11, 18.

Answer: Correct box plot with Q1=11.75, Median=13.5, Q3=15.5, Min=10, Max=18

Question 4: Which of the following box plots shows a distribution with a longer tail on the right?

Answer: Option B

Question 5: A student plots a box plot but forgets to include the minimum value. What impact does this mistake have on the interpretation of the data?

Answer: It can lead to an incorrect understanding of the data range and outliers, affecting the overall interpretation.

Question 6: Given two box plots, compare the spreads and medians. Plot the two box plots on the grid, then describe which distribution is more spread out and which has a higher median.

Answer: Student’s plotted box plots with explanation: e.g., Box plot 1 has a median of 7 and IQR of 4; Box plot 2 has a median of 5 and IQR of 2, so Box plot 1 is more spread out and has a higher median.

Question 7: A box plot shows the minimum as 5, Q1 as 8, median as 10, Q3 as 13, and maximum as 20. Identify a potential misconception students might have when interpreting this plot.

Answer: Students might assume the data is symmetric around the median, but the plot suggests data is skewed to the right due to the larger maximum.

Question 8: Error Analysis: A student plots a box plot with the incorrect Q1 value, placing it at 12 instead of 8. What effect does this mistake have on the interpretation of the distribution?

Answer: It will misrepresent the spread of the data, potentially making the distribution seem more dispersed or skewed incorrectly.

Question 9: Using the data set: 4, 5, 6, 7, 8, 9, 10, construct a box plot and explain what the features tell you about the distribution.

Answer: Q1=5.5, Median=7.5, Q3=8.5, Min=4, Max=10; shows a roughly symmetric distribution centered around 7.5.

Question 10: Challenge: Data set is skewed left: 15, 13, 12, 10, 8, 7, 5, 3. Draw the box plot and interpret the skewness.

Answer: Q1=7, Median=10, Q3=13, Min=3, Max=15; the box plot shows a longer tail on the left, indicating left skewness.