Question 1: Given the cumulative frequency table below, find the 50th percentile (median).

Answer: 24

Question 2: Construct a cumulative frequency table for the data: 3, 7, 8, 10, 12, 15. Then, determine the median.

Answer: The median is 10

Question 3: A class has the following cumulative frequency data: 0-10 (10), 10-20 (25), 20-30 (40), 30-40 (50). Find the median class and the median value.

Answer: 20-30, median = 25

Question 4: Plot on the grid the median for this dataset: 5, 7, 8, 12, 14, 16, 18, 20.

Answer: Median is 14

Question 5: The cumulative frequency table shows data for ages in a survey. Determine the 50th percentile age.

Answer: around 28 years

Question 6: In a dataset, the total number of data points is 60. If the 50th percentile is at position 30, at which data point in the ordered list does this median occur?

Answer: the 30th data point

Question 7: Explain why the median is not affected by extremely high or low values in a data set.

Answer: Because the median depends on the middle position, not the actual data values, extreme outliers do not change its position.

Question 8: A class of 40 students has the following scores summarized in a cumulative frequency table. Find the median score.

Answer: The median score is approximately 75

Question 9: Challenge: Given a large dataset with grouped data, describe the steps to find the 50th percentile using cumulative frequency.

Answer: Construct the cumulative frequency table, locate the median position (n/2), identify the median class, then interpolate within that class to find the median value.

Question 10: A common mistake is to find the average of the lower and upper bounds of the median class. Why is this incorrect, and what should be done instead?

Answer: It is incorrect because the median lies within the class interval, and proper interpolation using the cumulative frequency and class width provides a more accurate median value.