Question 1: Calculate the median, lower quartile, and upper quartile for the data set: 3, 7, 8, 5, 9, 12, 6, 10.

Answer: {"median":7.5,"lowerQuartile":5,"upperQuartile":10}

Question 2: Construct a box plot for the following data: 15, 22, 8, 13, 19, 17, 21, 16.

Answer: Box plot constructed on grid showing min=8, Q1=13, median=17, Q3=21, max=22

Question 3: Given two box plots, one with median at 12 and the other at 18, which distribution has a wider interquartile range? Explain your reasoning.

Answer: The box plot with median at 12 has a wider IQR if its box spans more units on the grid; otherwise, check the box lengths to determine.

Question 4: A data set's box plot shows Q1=20, median=25, Q3=30. If the minimum is 10 and maximum is 40, what can you say about the data distribution?

Answer: The data is spread out with some lower and higher values, possibly skewed; the interquartile range is 10 units.

Question 5: Calculate the interquartile range (IQR) for the data: 5, 7, 12, 15, 18, 21, 24.

Answer: See full answer key

Question 6: Plot the box plot for the data: 4, 9, 11, 13, 15, 18, 20. Use your grid to mark the minimum, Q1, median, Q3, and maximum.

Answer: Constructed box plot with min=4, Q1=9, median=13, Q3=18, max=20 on the grid.

Question 7: Two box plots have the same median and IQR but different ranges. What does this tell you about their data distributions?

Answer: They have similar middle 50% data but different overall spread, indicating different minimum and maximum values.

Question 8: A box plot shows an outlier at 50, which is much higher than the upper quartile. How should this be represented in the plot?

Answer: It should be shown as a point or asterisk beyond the Q3 + 1.5*IQR, indicating an outlier.

Question 9: Compare the distributions represented by two box plots: one with a median at 10 and Q1=8, Q3=12; another with median at 15 and Q1=13, Q3=17. Which is more skewed?

Answer: The first distribution may be slightly skewed if the box and whiskers are asymmetrical; compare box lengths and whisker positions.

Question 10: Identify and correct the mistake in this statement: 'The interquartile range (IQR) is the difference between the maximum and minimum values.'

Answer: The IQR is actually the difference between Q3 and Q1, not max and min.

Question 11: Given a box plot with a median of 14, Q1 of 10, and Q3 of 18, interpret what these tell you about the data distribution.

Answer: The data's middle 50% spans from 10 to 18 with a median at 14, indicating a fairly balanced distribution around the median.