Question 1: Given the cumulative frequency table below, determine the 50th percentile value. Class Interval | Cumulative Frequency 0-10 | 5 10-20 | 15 20-30 | 25 30-40 | 35 40-50 | 45 Use the data to find the approximate median.

Answer: 25

Question 2: Construct a cumulative frequency table for the following data set: Data points: 3, 7, 8, 5, 10, 12, 9, 6, 4, 11. Then, identify the 50th percentile value.

Answer: 8

Question 3: A class survey shows the ages of students as follows: 12, 14, 15, 13, 16, 14, 15, 16, 14, 13. Construct a grouped frequency table and find the median age (50th percentile).

Answer: 14

Question 4: Plot the graph of y=2x for x-values from 0 to 10 on the grid. Label the axes appropriately.

Answer: Students will draw the graph accordingly.

Question 5: A set of test scores has the following cumulative frequency: Score | Cumulative Frequency 50 | 4 60 | 9 70 | 15 80 | 20 90 | 24 Estimate the 50th percentile score.

Answer: 70

Question 6: Identify the mistake in this statement: 'The median is always the middle value of the data set.' Explain and correct it.

Answer: The median is the middle value when data is ordered, but in grouped data, it is estimated from the cumulative frequency table, not necessarily the middle data point.

Question 7: Using the grouped data: Ages 10-14 (10 students), 15-19 (15 students), 20-24 (12 students), determine the 50th percentile age.

Answer: 16

Question 8: A factory produces items with weights as follows (in grams): Weight (g) | Number of items 50-55 | 10 55-60 | 25 60-65 | 30 65-70 | 20 70-75 | 15 Construct the cumulative frequency table and find the median weight.

Answer: 61.5

Question 9: A data set is heavily skewed. Explain why the median (50th percentile) provides a better measure of central tendency than the mean in such cases.

Answer: Because the median is less affected by extreme values in skewed data, making it a more representative measure of central tendency.

Question 10: Determine the 50th percentile from the following data: 3, 7, 8, 5, 10, 12, 9, 6, 4, 11.

Answer: 8

Question 11: In a grouped frequency table, how do you estimate the median (50th percentile)? Describe the process briefly.

Answer: Identify the class where the 50th percentile lies using the cumulative frequency, then interpolate within that class to estimate the median.