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
Fresh day Alice, let's solve. Part 18(a): State the modal class. Step 1: Identify the frequency for each class interval. The frequencies are 4, 8, 10, 12, 4, 2. Step 2: Determine the class interval with the highest frequency. The highest frequency is 12, which corresponds to the class interval 30 - 40. The modal class is 30 - 40. Part 18(b)(i): Calculate the mean height of the plants. Step 1: Find the midpoint (x) for each class interval and calculate fx. | Heights of plants | Frequency (f) | Midpoint (x) | fx | |:------------------|:----------------|:---------------|:-----| | 0 - 10 | 4 | 5 | 20 | | 10 - 20 | 8 | 15 | 120 | | 20 - 30 | 10 | 25 | 250 | | 30 - 40 | 12 | 35 | 420 | | 40 - 50 | 4 | 45 | 180 | | 50 - 60 | 2 | 55 | 110 | | Total | f = 40 | | fx = 1100 | Step 2: Use the formula for the mean of grouped data. x = ( fx)/( f) x = (1100)/(40) x = 27.5 The mean height of the plants is 27.5 cm. Part 18(b)(ii): Calculate the standard deviation of the distribution. Step 1: Calculate x^2 and fx^2 for each class. | Heights of plants | Frequency (f) | Midpoint (x) | fx | x^2 | fx^2 | |:------------------|:----------------|:---------------|:-----|:------|:-------| | 0 - 10 | 4 | 5 | 20 | 25 | 1