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
The problem asks us to find two values: the weighted arithmetic mean (referred to as "the grade" in the question) and the simple arithmetic mean. Here are the given scores and their corresponding weights: • English: Score = 50, Weight = 4 • Biology: Score = 65, Weight = 2 • Mathematics: Score = 75, Weight = 1 • Physics: Score = 53, Weight = 3 • Chemistry: Score = 58, Weight = 3 Step 1: Calculate the sum of (score × weight) for the weighted arithmetic mean. (x_i · w_i) = (50 × 4) + (65 × 2) + (75 × 1) + (53 × 3) + (58 × 3) (x_i · w_i) = 200 + 130 + 75 + 159 + 174 (x_i · w_i) = 738 Step 2: Calculate the sum of the weights. w_i = 4 + 2 + 1 + 3 + 3 w_i = 13 Step 3: Calculate the weighted arithmetic mean (the grade). The formula for the weighted arithmetic mean is x_w = ( (x_i · w_i))/( w_i). x_w = (738)/(13) x_w ≈ 56.77 Step 4: Calculate the sum of the scores for the simple arithmetic mean. x_i = 50 + 65 + 75 + 53 + 58 x_i = 301 Step 5: Calculate the simple arithmetic mean. The number of subjects (n) is 5. The formula for the simple arithmetic mean is x = ( x_i)/(n). x = (301)/(5) x = 60.2 The weighted arithmetic mean (the grade) is approximately 56.77, and the simple arithmetic mean is 60.2. The grade (weighted arithmetic mean) is: 56.77 The arithmetic mean is: 60.2 Send me the next one 📸