Question 1: Given the data set: 3, 7, 8, 5, 10, 2, 9, find the minimum, Q1, median, Q3, and maximum. Write your answers clearly.

Answer: {"Q1":3.5,"Q3":9,"median":7.5,"maximum":10,"minimum":2}

Question 2: Construct a box plot for the data set: 15, 7, 22, 13, 19, 9, 17, 11. Show the five-number summary and draw the box plot on the grid.

Answer: Box plot with min=7, Q1=9, median=15, Q3=19, max=22.

Question 3: The five-number summary of a data set is: Minimum=4, Q1=6, Median=8, Q3=10, Maximum=12. Calculate the interquartile range (IQR).

Answer: See full answer key

Question 4: Identify the mistake in the following five-number summary: Minimum=2, Q1=4, Median=6, Q3=8, Maximum=5. Explain and correct it.

Answer: Maximum cannot be less than Q3. Corrected summary: Minimum=2, Q1=4, Median=6, Q3=8, Maximum=? (value should be ≥8).

Question 5: A teacher records the test scores of 12 students: 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110. Find the five-number summary, and describe what it tells you about the data distribution.

Answer: Min=55, Q1=65, Median=80, Q3=100, Max=110. Indicates a right-skewed distribution with higher scores at the upper end.

Question 6: Given the data: 4, 8, 6, 10, 12, 14, 16, 18, 20, find the median and quartiles. Show your working.

Answer: {"Q1":6,"Q3":18,"median":12}

Question 7: Plot a box plot on the grid for the data: 5, 7, 9, 11, 13, 15, 17, 19. Include the five-number summary.

Answer: Min=5, Q1=9, Median=13, Q3=17, Max=19.

Question 8: A data set has a minimum of 10, Q1 of 20, median of 30, Q3 of 40, and maximum of 50. What is the interquartile range, and what does this say about the data spread?

Answer: IQR = Q3 - Q1 = 20; indicates the middle 50% of data is spread over 20 units.

Question 9: A box plot shows the minimum as 12, Q1 as 16, median as 20, Q3 as 24, and maximum as 28. If a new data point 10 is added, how should the five-number summary change?

Answer: Minimum would decrease to 10; other values likely remain unchanged unless the point affects quartiles.

Question 10: Identify and correct the error in this five-number summary: Minimum=3, Q1=5, Median=7, Q3=9, Maximum=4.

Answer: Maximum cannot be less than Q3. Corrected summary: Maximum must be ≥9; likely the maximum is greater than 9.