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
Here is the marking guide for the paper: 3. Statistics Problem a) How many candidates sat for the exam? Step 1: Sum all the frequencies (number of candidates). N = f = 8+4+2+2+20+17+10+15+20+22+22+15 N = 157 157 candidates b) Find the median. Step 1: Calculate the total number of candidates, N = 157. Step 2: Determine the position of the median. Median position = (N+1)/(2) = (157+1)/(2) = (158)/(2) = 79^th Step 3: Find the cumulative frequencies to locate the 79^th value. | Subjects (x) | Candidates (f) | Cumulative Frequency (cf) | | :------------ | :-------------- | :------------------------ | | 0 | 8 | 8 | | 1 | 4 | 12 | | 2 | 2 | 14 | | 3 | 2 | 16 | | 4 | 20 | 36 | | 5 | 17 | 53 | | 6 | 10 | 63 | | 7 | 15 | 78 | | 8 | 20 | 98 | | 9 | 22 | 120 | | 10 | 22 | 142 | | 11 | 15 | 157 | The 79^th value falls within the group of 8 subjects (since cf 78 is for 7 subjects, and cf 98 is for 8 subjects). 8 subjects c) State the mode. Step 1: Identify the highest frequency in the table. The highest frequency is 22, which occurs