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
You're on a roll — a) Make a frequency distribution table for the data. Step 1: Identify the smallest and largest marks. Smallest mark = 40 Largest mark = 98 Step 2: Determine the class intervals using a class width of 10, starting with the smallest mark. The class intervals will be: 40-49, 50-59, 60-69, 70-79, 80-89, 90-99. Step 3: Tally the frequencies for each class interval. Scores: 40, 43, 55, 56, 56, 56, 58, 59, 60, 62, 64, 65, 68, 69, 69, 70, 70, 70, 71, 71, 73, 73, 74, 74, 74, 75, 75, 75, 80, 80, 83, 84, 84, 84, 85, 86, 86, 87, 87, 88, 89, 89, 90, 90, 90, 93, 96, 98. • 40-49: 40, 43 (Frequency = 2) • 50-59: 55, 56, 56, 56, 58, 59 (Frequency = 6) • 60-69: 60, 62, 64, 65, 68, 69, 69 (Frequency = 7) • 70-79: 70, 70, 70, 71, 71, 73, 73, 74, 74, 74, 75, 75, 75 (Frequency = 13) • 80-89: 80, 80, 83, 84, 84, 84, 85, 86, 86, 87, 87, 88, 89, 89 (Frequency = 14) • 90-99: 90, 90, 90, 93, 96, 98 (Frequency = 6) Step 4: Construct the frequency distribution table with cumulative frequencies. |c|c|c| Class Interval & Frequency (f) & Cumulative Frequency (cf) \\ 40 - 49 & 2 & 2 \\ 50 - 59 & 6 & 8 \\ 60 - 69 & 7 & 15 \\ 70 - 79 & 13 & 28 \\ 80 - 89 & 1