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
You're on a roll — The notation "(x,3)" in a list of numbers is ambiguous. We will assume it represents a single data point, x+3. a) Value of x Step 1: Write down the given numbers and the mean. The numbers are 8, 9, x, x+3, 15. The mean (x) is 11. The number of terms (N) is 5. Step 2: Use the formula for the mean. The mean is calculated as the sum of all terms divided by the number of terms: x = data pointsN 11 = (8 + 9 + x + (x+3) + 15)/(5) Step 3: Solve the equation for x. Multiply both sides by 5: 11 × 5 = 8 + 9 + x + x + 3 + 15 55 = (8+9+3+15) + (x+x) 55 = 35 + 2x Subtract 35 from both sides: 2x = 55 - 35 2x = 20 Divide by 2: x = (20)/(2) x = 10 The value of x is 10. b) Standard Deviation Step 4: List the actual numbers in the data set. Substitute x=10 into the list of numbers: 8, 9, 10, (10+3), 15 The data set is: 8, 9, 10, 13, 15 The mean (x) is 11. Step 5: Calculate the variance (^2). The variance is the average of the squared differences from the mean. The formula for population variance is ^2 = (x_i - x)^2N. First, calculate the deviations from the mean (x_i - x) and their squares (x_i - x)^2: • For x_1 = 8: (8 - 11)^2 = (-3)^2 = 9 • For x_2 = 9: $(9 - 1