Question 1: Calculate the median, range, and interquartile range (IQR) for the data set: 12, 15, 14, 16, 13, 14, 15, 17.

Answer: {"IQR":2,"range":5,"median":14.5}

Question 2: Draw a box plot for the following data: 8, 10, 12, 14, 16, 18, 20.

Answer: Student draws a box plot with median 14, Q1 at 10, Q3 at 18, and whiskers to 8 and 20.

Question 3: Two box plots are shown: Plot A has a median of 12, Q1 of 9, Q3 of 15; Plot B has a median of 14, Q1 of 10, Q3 of 18. Which distribution is more spread out? Justify your answer.

Answer: Plot B is more spread out because it has larger interquartile range (8 vs. 6).

Question 4: From the box plot shown, estimate the minimum, maximum, median, Q1, and Q3. The data points are spread from 5 to 25 with median at 15.

Answer: {"Q1":10,"Q3":20,"median":15,"maximum":25,"minimum":5}

Question 5: Identify the common mistake in interpreting box plots and explain how to avoid it.

Answer: A common mistake is confusing the median line with the mean. To avoid this, remember the median is the middle value, not the average.

Question 6: Given two box plots, compare their medians and describe what this indicates about the two data sets.

Answer: The box plot with the higher median indicates the typical value in that data set is greater.

Question 7: Calculate the interquartile range (IQR) for the data set: 22, 25, 27, 30, 31, 33, 35.

Answer: See full answer key

Question 8: Construct a box plot for data: 5, 7, 9, 11, 13, 15, 17. Label the median, Q1, Q3, minimum, and maximum on your plot.

Answer: Median at 11, Q1 at 7, Q3 at 15, whiskers to 5 and 17.

Question 9: A box plot shows a median of 20 with an IQR of 8. If the lower quartile (Q1) is at 16, what is the value of the upper quartile (Q3)?

Answer: See full answer key

Question 10: Identify a real-world scenario where comparing two distributions using box plots would be useful. Briefly explain why.

Answer: Comparing test scores from two different classes helps identify which class has higher or more consistent performance.