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: Calculate the total number of candidates. The total number of candidates is the sum of all frequencies. f = 8 + 4 + 2 + 2 + 20 + 17 + 10 + 15 + 20 + 25 + 22 + 15 = 160 a) The total number of candidates who sat for the exam is 160. Step 2: Find the median. The total number of candidates is N = 160. The position of the median is (N+1)/(2) = (160+1)/(2) = (161)/(2) = 80.5. We need to find the value corresponding to the 80.5th candidate. We use cumulative frequencies: • 0 subjects: 8 candidates • 1 subject: 8+4=12 candidates • 2 subjects: 12+2=14 candidates • 3 subjects: 14+2=16 candidates • 4 subjects: 16+20=36 candidates • 5 subjects: 36+17=53 candidates • 6 subjects: 53+10=63 candidates • 7 subjects: 63+15=78 candidates • 8 subjects: 78+20=98 candidates The 80.5th candidate falls within the group of candidates who passed 8 subjects. b) The median number of subjects passed is 8. Step 3: State the mode. The mode is the number of subjects passed with the highest frequency. Looking at the "Number of candidates" row, the highest frequency is 25, which corresponds to 9 subjects passed. c) The mode number of subjects passed is 9. Step 4: Calculate the mean number of subjects passed. The mean is given by ( fx)/( f). First, calculate fx: fx = (0 × 8) + (1 × 4) + (2 × 2) + (3 × 2) + (4 × 2