Question 1: Given the data: 5, 7, 8, 10, 12, 15, construct the cumulative frequency table for these values and state the total number of data points.

Answer: Values: 5,7,8,10,12,15; Cumulative counts: 1,2,3,4,5,6; Total: 6

Question 2: Calculate the cumulative frequency for a class interval where 12 students scored less than 60, based on the following data: 10, 15, 20, 25, 30, 35, 40, 50, 55, 60, 65, 70.

Answer: 12 students scored less than 60

Question 3: Construct the cumulative frequency table for the following data: 3, 5, 7, 9, 11, 13, 15. Then plot the cumulative frequency graph on the grid.

Answer: Constructed table: values and cumulative counts; Student plots points accordingly.

Question 4: Explain how to find the median class from a cumulative frequency table and perform this for the data: 2, 4, 6, 8, 10, 12, 14, 16.

Answer: Find the total, locate the middle value's position, identify the class interval containing this position.

Question 5: A survey records the times (in minutes) students arrive at school: 8, 10, 12, 12, 15, 15, 15, 18, 20, 22. Construct the cumulative frequency table and interpret how many students arrive before 15 minutes.

Answer: Cumulative frequency up to 15 minutes: 7 students arrive before 15 minutes

Question 6: A cumulative frequency table shows that 25 students scored less than 80 out of 100. If the total number of students is 50, what fraction scored 80 or more?

Answer: 25 students scored 80 or more; fraction: 25/50 = 1/2

Question 7: Using the table: Scores: 50, 60, 70, 80, 90, 100; cumulative frequencies: 2, 4, 7, 10, 12, 15. Find the median score.

Answer: Median position = (15+1)/2=8th; median score roughly 80.

Question 8: Identify and correct the mistake in this cumulative frequency table: Values: 1,2,3,4; Cumulative counts: 1,3,6,10.

Answer: The counts are cumulative; the individual data points are incorrect; correct counts should be sequential or based on raw data.

Question 9: A set of data: 2, 4, 4, 6, 8, 10, construct the cumulative frequency table and identify how many values are less than 7.

Answer: Values less than 7: 2,4,4,6; Total: 4

Question 10: A factory records the number of defective items per batch: 0, 1, 2, 2, 3, 4. Construct the cumulative frequency table and find how many batches had 2 or fewer defects.

Answer: Batches with 2 or fewer defects: 5

Question 11: Challenge: The data set: 5, 8, 8, 10, 12, 12, 12, 15, construct the cumulative frequency table and determine the modal class interval.

Answer: Cumulative counts: 1,3,5,6,8; Mode: 12 (most frequent value).