Question 1: Given a cumulative frequency table, identify the correct position of Q1, Q2, and Q3. The total number of data points is 60. The cumulative frequencies are 5, 15, 30, 45, 60. Which cumulative frequency corresponds to Q2?

Answer: 30

Question 2: A student calculates Q3 by taking 75% of the total data points. Is this method correct? Explain your reasoning.

Answer: No, Q3 is the third quartile and should be found at 75% of the position in the ordered data, but it is not simply 75% of total points; it involves locating the position in the cumulative frequency.

Question 3: In the table, the cumulative frequency just before Q1's position is 10, and the cumulative frequency at Q1's position is 15. The total number of data points is 50. Calculate the approximate value of Q1 assuming the class width is 4.

Answer: Q1 ≈ class lower bound + [(Q1 position - previous cumulative frequency) / frequency at Q1] × class width

Question 4: A cumulative frequency table shows total 80 data points. The cumulative frequency just before Q2 is 40, and at Q2 is 50. The class width is 5. Find the approximate value of Q2.

Answer: Q2 ≈ lower class limit + [(Q2 position - previous cumulative frequency) / frequency at Q2] × class width

Question 5: A common misconception is to find Q1 by taking 25% of the total data points and then locating that point. Why is this approach incorrect?

Answer: Because quartiles are located at specific positions in the ordered data, not just a percentage of total points; the position must be within the cumulative frequency, not a simple percentage.

Question 6: In a cumulative frequency table, the total number of data points is 100. Q3 is at cumulative frequency 75. If the class width is 6, and the previous cumulative frequency before Q3 is 60, estimate the value of Q3.

Answer: Q3 ≈ lower class limit + [(Q3 position - previous cumulative frequency) / frequency at Q3] × class width

Question 7: Explain a common mistake students make when interpolating to find quartiles from a cumulative frequency table.

Answer: Students often incorrectly assume that the quartile position is always at the same fraction of the total data, without considering the exact cumulative frequencies or interpolating properly between class limits.

Question 8: Plot the cumulative frequency distribution for the following data points: 10, 20, 30, 40, 50. Use the grid to draw the graph, marking Q1, Q2, and Q3 on the plot.

Answer: Student draws the cumulative frequency curve, marks the positions corresponding to 25%, 50%, 75% of total data points, and labels Q1, Q2, Q3 accordingly.

Question 9: A cumulative frequency table has the following data: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. Find Q1, Q2, and Q3 using proper methods.

Answer: Q1 at position 25 (approx), Q2 at position 50, Q3 at position 75, then interpolate accordingly.

Question 10: Challenge: Given a cumulative frequency table with irregular class widths, explain how to accurately find Q1, Q2, and Q3.

Answer: Identify the positions of Q1, Q2, Q3 based on total data points, interpolate within the specific class intervals considering varying widths, and avoid assuming equal class widths.