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
Hey Elijah, good to see you again. To solve this problem, we first need to organize the given data and calculate the midpoints of each class interval. We will also calculate the products fd and fd^2 for the assumed mean method. Given data: Length (cm) | No. of rods (f) ------------|---------------- 8-10 | 4 11-13 | 7 14-16 | 11 17-19 | 15 20-22 | 8 23-25 | 5 26-28 | 3 Let A = 18 be the assumed mean. We calculate the midpoint (x) for each class, the deviation d = x - A, fd, and fd^2. | Length (cm) | f | Midpoint (x) | d = x - 18 | fd | fd^2 | |:-----------:|:---:|:--------------:|:------------:|:----:|:------:| | 8-10 | 4 | 9 | -9 | -36 | 324 | | 11-13 | 7 | 12 | -6 | -42 | 252 | | 14-16 | 11 | 15 | -3 | -33 | 99 | | 17-19 | 15 | 18 | 0 | 0 | 0 | | 20-22 | 8 | 21 | 3 | 24 | 72 | | 23-25 | 5 | 24 | 6 | 30 | 180 | | 26-28 | 3 | 27 | 9 | 27 | 243 | | Total | f = 53 | | | fd = -30 | fd^2 = 1170 | a) State the frequency of the modal class. Step 1: Identify the modal class. The modal class is the class interval with the highest frequency. From the table, the highest frequency is 15, which corresponds to the class interval 17-19. Step 2: State the frequency. The frequency of the modal class is 15. The frequency of the modal class is 15. b) Using 18 as an assumed mean, calculate: i) Actual mean Step 1: Use the formula for the actual mean with an assumed mean. The formula is x = A + ( fd)/( f). Step 2: Substitute the values. x = 18 + (-30)/(53) x = 18 - 0.5660377... x ≈ 17.434 The actual mean is 17.434 cm. ii) Variance Step 1: Use the formula for variance with an assumed mean. The formula is ^2 = ( fd^2)/( f) - (( fd)/( f))^2. Step 2: Substitute the values. ^2 = (1170)/(53) - ((-30)/(53))^2 ^2 = 22.075471698 - (-0.5660377358)^2 ^2 = 22.075471698 - 0.320409009 ^2 = 21.755062689 ^2 ≈ 21.755 The variance is 21.755 cm^2. iii) Standard deviation Step 1: Use the formula for standard deviation. The formula is = sqrt(^2). Step 2: Substitute the variance value. = sqrt(21.755062689) = 4.6642319... ≈ 4.664 The standard deviation is 4.664 cm. Send me the next one 📸