Question 1: A pie chart shows the favorite sports of 120 students. If 30 students like football, what is the frequency (number of students) for basketball if its sector represents 90 degrees?

Answer: 30

Question 2: Calculate the frequency of students who prefer tennis if the sector for tennis is 60 degrees and the total number of students is 150.

Answer: 25

Question 3: A pie chart with total frequency 200 has a sector of 45 degrees. What is the frequency for that category?

Answer: 25

Question 4: A sector representing 120 students corresponds to a 72-degree slice of a pie chart. Confirm the total number of students in the survey.

Answer: 250

Question 5: In a pie chart, a sector of 30 degrees represents 50 students. Identify and correct the common mistake if someone claims the total number of students is 300.

Answer: Incorrect; total students = (50/30) * 360 = 600, so total is 600, not 300.

Question 6: A pie chart shows the following sectors: Sports (100°), Music (80°), Arts (60°), and Others. Find the frequency for Arts if the total is 180 students.

Answer: 30

Question 7: Identify the error in this statement: 'A sector of 45° corresponds to 10 students, so total students must be 80.'

Answer: Incorrect; total = (10/45)*360=80, which is correct in this case, but many students might miscalculate.

Question 8: Construct a sector in a pie chart representing 25% of the total 240 students. Calculate the degrees of this sector and the number of students represented.

Answer: 90 degrees, 60 students

Question 9: A pie chart has a sector of 150° representing 75 students. What is the total number of students? Show your working.

Answer: Total = (75/150)*360=180

Question 10: A student incorrectly calculates the frequency for a sector of 90° as 40 students when the total is 180. Explain the mistake and provide the correct frequency.

Answer: Mistake: They used 90°/360°* total students, which is incorrect; correct: (total students) = (40/90)*360=160.