This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: First quartile of the distribution (Question 27) Total number of students n=50. Position of the first quartile: (n+1)/(4)=(51)/(4)=12.75. From the cumulative frequency curve, a cumulative frequency of 12.75 corresponds to 35 marks. First quartile = 35 marks. 35 marks Step 2: Modal class of the distribution (Question 28) The modal class is the class interval in which the cumulative frequency curve has the steepest slope (highest frequency). From the graph, the greatest rise occurs between 50 marks and 60 marks. Modal class = 50-60 marks. 50-60 marks Step 3: Probability that a student gets 50 or more marks (Question 29) From the graph, cumulative frequency up to 50 marks =25. Number of students getting 50 or more marks =50-25=25. Probability =(25)/(50)=(1)/(2). Probability =(1)/(2). (1)/(2) Step 4: Number of students who got 75 marks or more (Question 30) From the graph (near upper quartile), cumulative frequency up to 75 marks =38. Number of students getting 75 marks or more =50-38=12. 12 students. 12 students