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 solution to the problem. First, let's reconstruct the complete frequency distribution table based on the given information and the student's work for part (a). The total number of students is 100. The given frequencies are: 6, 9, 12, y, 20, 7, 4, z (where z is the frequency for 70 x < 80). *a) Determine the value of y. The sum of all frequencies must be 100. From the student's work, 100 - 86 = 14, which implies y=14. This means the sum of all other frequencies (excluding y) is 86. Let's verify this by finding z. 6 + 9 + 12 + 20 + 7 + 4 + z = 86 58 + z = 86 z = 86 - 58 = 28. So, the frequency for the class 70 x < 80 is 28. Now, let's sum all frequencies with y=14 and z=28: 6 + 9 + 12 + 14 + 20 + 7 + 4 + 28 = 100. This is correct. The complete frequency distribution table is: | Marks (x) | No. of students (f) | Midpoint (x_m) | fx_m |