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: Identify the modal class and formula. The given mode is 39. Since 39 falls in the class interval 35-45, this is our modal class. The formula for the mode of grouped data is: Mode = L + ( (f_1 - f_0)/(2f_1 - f_0 - f_2) ) × h Where: L = lower limit of the modal class h = size of the class interval f_1 = frequency of the modal class f_0 = frequency of the class preceding the modal class f_2 = frequency of the class succeeding the modal class Step 2: Extract values from the table. From the modal class 35-45: L = 35 h = 45 - 35 = 10 f_1 = 7 (frequency of 35-45) f_0 = x (frequency of 25-35) f_2 = 4 (frequency of 45-55) The given mode is 39. Step 3: Substitute the values into the mode formula. 39 = 35 + ( (7 - x)/(2(7) - x - 4) ) × 10 Step 4: Solve the equation for x. First, subtract 35 from both sides: 39 - 35 = ( (7 - x)/(14 - x - 4) ) × 10 4 = ( (7 - x)/(10 - x) ) × 10 Divide both sides by 10: (4)/(10) = (7 - x)/(10 - x) (2)/(5) = (7 - x)/(10 - x) Cross-multiply: 2(10 - x) = 5(7 - x) 20 - 2x = 35 - 5x Rearrange the terms to solve for x: 5x - 2x = 35 - 20 3x = 15 x = (15)/(3) x = 5 The value of the unknown frequency x is 5. Send me the next one 📸