Question 1: Given the cumulative frequency table below, find the value of the first quartile (Q1).

Answer: 15

Question 2: Calculate the median (Q2) for the following data set represented by a cumulative frequency table.

Answer: 27

Question 3: From the cumulative frequency table, determine the value of the third quartile (Q3).

Answer: 38

Question 4: Construct a cumulative frequency table for the data: 12, 15, 20, 22, 25, 30, 35, 40. Then find Q1, Q2, and Q3.

Answer: Q1=15, Q2=25, Q3=35

Question 5: A class's test scores are summarized in a cumulative frequency table. If the total number of students is 60, what is the value of Q2 (the median score)?

Answer: 75

Question 6: Explain why Q2 is also called the median of the data set.

Answer: Q2 divides the data into two equal halves, so it is the median.

Question 7: Plot the cumulative frequency curve for the data set: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Use the grid to draw the curve.

Answer: Student draws the curve; no numerical answer.

Question 8: A dataset has Q1 = 12, Q2 = 20, and Q3 = 35. If a new data point of 40 is added, how do the quartiles change? Explain briefly.

Answer: Adding 40 likely increases Q3, while Q1 and Q2 may stay the same or slightly increase; depends on the data distribution.

Question 9: Identify and correct the mistake in this calculation: Q1 = 25, but the cumulative frequency at 25 is 18, which is less than 25. Why is this wrong?

Answer: Q1 corresponds to the value at the 25th percentile, not the cumulative frequency; need to interpolate if necessary.

Question 10: Using the data set: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, find Q1, Q2, and Q3.

Answer: Q1=30, Q2=55, Q3=80

Question 11: Challenge: Given a cumulative frequency table where the total is 100, and the values of Q1, Q2, Q3 are 20, 50, and 75 respectively, explain how the shape of the data distribution affects these quartiles.

Answer: A symmetric distribution will have Q1, Q2, Q3 evenly spaced; skewed data will shift the quartiles accordingly.