Question 1: Given the cumulative frequency table below, find the median (50th percentile) value: Class interval: 10-20, 20-30, 30-40, 40-50, 50-60 Cumulative frequency: 5, 12, 20, 27, 30

Answer: 35

Question 2: Calculate the median class for the data given below: Class intervals: 5-15, 15-25, 25-35, 35-45 Cumulative frequencies: 8, 20, 28, 32

Answer: 15-25

Question 3: A dataset has the following cumulative frequency table: Class: 0-10, 10-20, 20-30, 30-40, 40-50 Cumulative frequency: 4, 9, 15, 22, 30 Estimate the median value.

Answer: 20

Question 4: Plot the graph of y = 2x for x values from 0 to 10 on the grid. Use this to approximate the median in a dataset where the median is at y=10.

Answer: x=5

Question 5: Construct a cumulative frequency curve using the data: Class intervals: 0-10, 10-20, 20-30, 30-40 Cumulative frequencies: 3, 8, 14, 20 Estimate the median.

Answer: 20

Question 6: In a survey, the cumulative frequency table shows that 60 students scored below 45 marks. The total number of students is 120. What is the median score?

Answer: 45

Question 7: Identify and correct the mistake in this median calculation: "Median = (n/2)th value = (120/2) = 60th student. The median score is 50."

Answer: The mistake is equating the position (60th student) to a score directly. Need to find the corresponding score from the cumulative frequency table, not just the position.

Question 8: A class's cumulative frequency data indicates that the median score is at the 75th percentile. If the total number of students is 200, how many students scored below the median?

Answer: 150

Question 9: A dataset's cumulative frequency table shows the median falling between two class boundaries. Explain how to accurately estimate the median value in this case.

Answer: Use linear interpolation between the cumulative frequencies at the boundaries to estimate the median within the class interval.

Question 10: Given this cumulative frequency table, determine the 50th percentile: Class: 20-30, 30-40, 40-50, 50-60, 60-70 Cumulative frequency: 6, 14, 22, 28, 30

Answer: 45

Question 11: Challenge: For a dataset with uneven class widths, explain how the calculation of the median from the cumulative frequency table differs.

Answer: You need to account for the variable class widths, often by interpolating within the class containing the median, adjusting calculations based on class size.