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
Step 1: Calculate the class mark (x_i) for each class interval. The class mark is the midpoint of the class interval. For 50 - 52: x_1 = (50+52)/(2) = 51 For 53 - 55: x_2 = (53+55)/(2) = 54 For 56 - 58: x_3 = (56+58)/(2) = 57 For 59 - 61: x_4 = (59+61)/(2) = 60 For 62 - 64: x_5 = (62+64)/(2) = 63 Step 2: Choose an assumed mean (A) and calculate the class size (h). Let's choose the middle class mark as the assumed mean, A = 57. The class size h is the difference between consecutive class marks, h = 54 - 51 = 3. Step 3: Calculate the deviation (d_i = x_i - A) and the step-deviation (u_i = (d_i)/(h)) for each class. Step 4: Calculate the product of frequency and step-deviation (f_i u_i). We can organize these calculations in a table: |c|c|c|c|c|c| Number of mangoes & Number of boxes (f_i) & Class Mark (x_i) & d_i = x_i - 57 & u_i = (d_i)/(3) & f_i u_i \\ 50 - 52 & 15 & 51 & -6 & -2 & -30 \\ 53 - 55 & 110 & 54 & -3 & -1 & -110 \\ 56 - 58 & 135 & 57 & 0 & 0 & 0 \\ 59 - 61 & 115 & 60 & 3 & 1 & 115 \\ 62 - 64 & 25 & 63 & 6 & 2 & 50 \\ Total & f_i = 400 & & & & f_i u_i = 25 \\ Step 5: Apply the formula for the mean using the step-deviation method. The formula for the mean (x) using the step-deviation method is: x = A + (( f_i u_i)/( f_i)) h Substitute the values: x = 57 + ((25)/(400)) × 3 x = 57 + ((1)/(16)) × 3 x = 57 + (3)/(16) x = 57 + 0.1875 x = 57.1875 The method chosen is the Step-Deviation Method. The mean number of mangoes kept in a packing box is 57.1875 mangoes.