Question 1: Calculate the median (50th Percentile) for the following cumulative frequency table: Class Interval | Cumulative Frequency 0-10 | 5 10-20 | 15 20-30 | 25 30-40 | 35 40-50 | 50

Answer: 24

Question 2: A grouped frequency table shows the number of students scoring in different ranges. The total number of students is 80. If the cumulative frequency at 50 marks is 40, what is the 50th percentile score?

Answer: 50

Question 3: Explain why incorrectly interpolating between class boundaries might lead to errors in calculating the 50th Percentile.

Answer: Incorrect interpolation can lead to inaccurate median estimates because the true median might be closer to one boundary than the other, and assuming a uniform distribution within classes can be false.

Question 4: Given a cumulative frequency table, identify the mistake in the following calculation of the median: "Median = lower boundary of median class + ( (N/2 - cumulative frequency before median class) / frequency of median class ) × class width" where the cumulative frequency before median class was mistakenly taken as 20 instead of 15.

Answer: The mistake would lead to an incorrect median calculation; the correct cumulative frequency before the median class should be 15, not 20.

Question 5: Plot the graph of y = 2x for x-values from 0 to 10 on the grid. Use this to estimate the 50th percentile if the cumulative frequency data is proportional to y.

Answer: At y = 20, x = 10; the estimated median is at x = 5.

Question 6: A survey reports the cumulative number of people who have a certain level of income. If the total number of people surveyed is 200, and the cumulative frequency at 30,000 units income is 100, what is the income at the 50th percentile?

Answer: 30,000

Question 7: Construct a triangle with sides corresponding to the class widths and cumulative frequencies to visually estimate the median from the data provided.

Answer: Students should draw a cumulative frequency graph and identify the median class by interpolation.

Question 8: Identify the common misconception when students assume the 50th percentile always corresponds to the middle of the data range without considering grouped data.

Answer: They overlook the effect of data grouping and that the median is based on cumulative frequency, not necessarily the midpoint of the class intervals.

Question 9: A data set has the following cumulative frequencies: 20, 45, 65, 80, 100. Find the 50th percentile and explain your calculation steps.

Answer: Total N=100, half=50. The 50th percentile is in the second class interval. Using interpolation, median ≈ lower boundary + ((N/2 - cumulative frequency before median class)/frequency of median class) × class width.

Question 10: A common error is selecting the class where the cumulative frequency just exceeds N/2 without performing interpolation. Why is this approach sometimes inaccurate?

Answer: Because it ignores the distribution within the class and can lead to an over- or under-estimate of the median, especially if the class is wide.