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
Okay, let's continue with the calculations for part (b) and (c). b) Using the data (as a graph is not available, we use linear interpolation): b)(i) The median mark: The median is the 50^th percentile. Step 1: Determine the position of the median. Position = (N)/(2) = (80)/(2) = 40^th Step 2: Identify the median class. The 40^th student falls in the 50-59 class, as the cumulative frequency goes from 37 (for 40-49) to 57 (for 50-59). Step 3: Apply the median formula. The lower class boundary (L) for the 50-59 class is 49.5. The cumulative frequency before the median class (C_f) is 37. The frequency of the median class (f_m) is 20. The class width (c) is 59.5 - 49.5 = 10. Median = L + ((N)/(2) - C_ff_m) × c Median = 49.5 + ((40 - 37)/(20)) × 10 Median = 49.5 + ((3)/(20)) × 10 Median = 49.5 + 1.5 Median = 51 marks b)(ii) The 60^th percentile mark: Step 1: Determine the position of the 60^th percentile. Position = (60)/(100) × N = (60)/(100) × 80 = 48^th Step 2: Identify the percentile class. The 48^th student falls in the 50-59 class, as the cumulative frequency goes from 37 to 57. Step 3: Apply the percentile formula. The lower class boundary (L) for the 50-59 class is 49.5. The cumulative frequency before this class (C_f) is 37. The frequency of this class (f_p) is 20. The class width (c) is 10. P_60 = L + ((60N)/(100) - C_ff_p) × c P_60 = 49.5 + ((48 - 37)/(20)) × 10 P_60 = 49.5 + ((11)/(20)) × 10 P_60 = 49.5 + 5.5 P_60 = 55 marks c) If the pass mark was 50%, what percentage of students passed? Step 1: Identify the number of students who scored 50% or more. Students scoring 50% or more are those in the classes 50-59, 60-69, 70-79, 80-89, and 90-99. Number of students passed = 20 + 11 + 7 + 3 + 2 = 43. Step 2: Calculate the percentage of students who passed. Total number of students = 80. Percentage passed = Number of students passedTotal number of students × 100\% Percentage passed = (43)/(80) × 100\% Percentage passed = 0.5375 × 100\% Percentage passed = 53.75\% That's 2 down. 3 left today — send the next one.