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 — Here are the calculations for Question 1: First, we prepare a table to find the midpoints (x), fx, fx^2, and cumulative frequencies (cf). The class intervals are given as 8-12, 13-17, 18-22, 23-27, 28-32. To find the class boundaries, we adjust by 0.5. The class width (w) for each interval is 12.5 - 7.5 = 5. | Class Interval | Class Boundaries | Midpoint (x) | Frequency (f) | fx | x^2 | fx^2 | Cumulative Frequency (cf) | |:---------------|:-----------------|:-------------|:--------------|:---|:------|:-------|:--------------------------| | 8-12 | 7.5-12.5 | 10 | 6 | 60 | 100 | 600 | 6 | | 13-17 | 12.5-17.5 | 15 | 8 | 120| 225 | 1800 | 14 | | 18-22 | 17.5-22.5 | 20 | 12 | 240| 400 | 4800 | 26 | | 23-27 | 22.5-27.5 | 25 | 8 | 200| 625 | 5000 | 34 | | 28-32 | 27.5-32.5 | 30 | 6 | 180| 900 | 5400 | 40 | | Total | | | f = 40 | fx = 800 | | fx^2 = 17600 | | Total frequency N = f = 40. a) The mean weight Step 1: Use the formula for the mean of grouped data. x = ( fx)/(N)