Question 1: In the following grouped data on the number of books read by students in a month, identify the modal class: Class intervals: 0-2, 3-5, 6-8, 9-11 Frequencies: 5, 12, 8, 3

Answer: 3-5

Question 2: Calculate the total number of students if the data above represents all students surveyed.

Answer: 28

Question 3: Explain why the class 3-5 is considered the modal class in the given data.

Answer: Because it has the highest frequency (12), making it the most common number of books read.

Question 4: Plot the frequency distribution on the grid for the class intervals given.

Answer: Students plot bars at 0-2:5, 3-5:12, 6-8:8, 9-11:3.

Question 5: What is the modal class for this data? Show your calculation.

Answer: 3-5

Question 6: If 4 students are added to the class 6-8, how does this affect the modal class? Explain.

Answer: Adding 4 more students increases the frequency of 6-8 to 12, tying with 3-5, so now the modal class is 3-5 and 6-8.

Question 7: A new survey shows the following class intervals and frequencies: 0-2: 4, 3-5: 15, 6-8: 10, 9-11: 6. Find the new modal class.

Answer: 3-5

Question 8: Identify and correct the mistake: A student says the modal class is 0-2 because it has the lowest frequency.

Answer: The mistake is that the modal class has the highest frequency, not the lowest. The correct modal class is 3-5.

Question 9: Using the original data, determine the class interval with the lowest frequency and suggest a reason why.

Answer: 9-11; because fewer students read that many books.

Question 10: Construct a frequency table for the following grouped data: Class intervals: 0-2, 3-5, 6-8, 9-11 Frequencies: 4, 9, 7, 2

Answer: See table: 0-2:4, 3-5:9, 6-8:7, 9-11:2.

Question 11: Challenge: A class has the following grouped data for test scores: Class intervals: 0-49, 50-59, 60-69, 70-79, 80-89 Frequencies: 3, 7, 10, 8, 2 Find the modal class and explain your reasoning.

Answer: The modal class is 60-69 because it has the highest frequency (10).