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
Welcome back Chimuka — missed you this week. a) To calculate the standard deviation for grouped data, we first find the midpoint (x) for each class, then calculate fx and fx^2. Step 1: Calculate midpoints (x), fx, and fx^2. | Amount (K) | No. of farmers (f) | Midpoint (x) | fx | x^2 | fx^2 | |:-------------|:---------------------|:---------------|:-----|:------|:-------| | 0 < x 100 | 5 | 50 | 250 | 2500 | 12500 | | 100 < x 200 | 16 | 150 | 2400 | 22500 | 360000 | | 200 < x 300 | 17 | 250 | 4250 | 62500 | 1062500 | | 300 < x 400 | 17 | 350 | 5950 | 122500 | 2082500 | | 400 < x 500 | 14 | 450 | 6300 | 202500 | 2835000 | | 500 < x 600 | 12 | 550 | 6600 | 302500 | 3630000 | | 600 < x 700 | 7 | 650 | 4550 | 422500 | 2957500 | | 700 < x 800 | 2 | 750 | 1500 | 562500 | 1125000 | | Total | f = 90 | | fx = 31800 | | fx^2 = 14065000 | Step 2: Apply the formula for standard deviation (). = sqrt(( fx^2)/( f) - (( fx)/( f))^2) Substitute the calculated sums: = sqrt((14065000)/(90) - ((31800)/(90))^2) Step 3: Calculate the values. = sqrt(156277.777... - (353.333...)^2) = sqrt(156277.777... - 124844.444...) = sqrt(31433.333...) ≈ 177.2945 Rounding to three significant figures: ≈ 177 K b) i) To complete the cumulative frequency table, add the frequencies sequentially. | Amount (K) | 0 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | |:-------------|:--------|:----------|:----------|:----------|:----------|:----------|:----------|:----------|:----------| | Frequency | 0 | 5 | 21 | 38 | 55 | 69 | 81 | 88 | 90 | ii) To draw a smooth cumulative frequency curve: • Plot the upper class boundaries against their corresponding cumulative frequencies. The points to plot are (0, 0), (100, 5), (200, 21), (300, 38), (400,