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
Okay, semiunkamara25, let's tackle question 4. Part (i): Find the mean of the numbers 5+x_1, 5+x_2, 5+x_3, 5+x_4. Step 1: Use the given mean to find the sum of x_1, x_2, x_3, x_4. The mean of x_1, x_2, x_3, x_4 is 7. The formula for the mean is sum of numberscount of numbers. (x_1 + x_2 + x_3 + x_4)/(4) = 7 Multiply both sides by 4 to find the sum: x_1 + x_2 + x_3 + x_4 = 7 × 4 = 28 Step 2: Calculate the sum of the new set of numbers. The new numbers are 5+x_1, 5+x_2, 5+x_3, 5+x_4. Their sum is: (5+x_1) + (5+x_2) + (5+x_3) + (5+x_4) = (5+5+5+5) + (x_1+x_2+x_3+x_4) = 20 + 28 = 48 Step 3: Calculate the mean of the new set of numbers. There are 4 numbers in the new set. Mean = Sum of new numbersCount of new numbers = (48)/(4) = 12 The mean of the numbers 5+x_1, 5+x_2, 5+x_3, 5+x_4 is 12. Part (ii): Calculate the mean age of the class from the frequency table. Step 1: Calculate the sum of (age × frequency) for all age groups. Multiply each age by its corresponding frequency: • For age 12: 12 × 8 = 96 • For age 13: 13 × 10 = 130 • For age 14: 14 × 4 = 56 • For age 15: 15 × 2 = 30 Sum of (age × frequency) = 96 + 130 + 56 + 30 = 312 Step 2: Calculate the total frequency (total number of pupils). Add all the frequencies: Total frequency = 8 + 10 + 4 + 2 = 24 Step 3: Calculate the mean age. The mean age is the sum of (age × frequency) divided by the total frequency: Mean age = Sum of (age × frequency)Total frequency = (312)/(24) = 13 The mean age of the class is 13 years. That's 2 down. 3 left today — send the next one.