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 — a) Step 1: Write the formula for the mean. The mean of a set of numbers is the sum of the numbers divided by the count of the numbers. The given numbers are 8, 9, x, (x+1), 15. There are 5 numbers. The mean is 11. Mean = ( x_i)/(N) 11 = (8 + 9 + x + (x+1) + 15)/(5) Step 2: Solve for x. Multiply both sides by 5: 11 × 5 = 8 + 9 + x + x + 1 + 15 55 = 33 + 2x Subtract 33 from both sides: 55 - 33 = 2x 22 = 2x Divide by 2: x = (22)/(2) x = 11 b) Step 3: List the numbers with the value of x. Substitute x=11 into the set of numbers: 8, 9, 11, (11+1), 15 The numbers are 8, 9, 11, 12, 15. The mean () is given as 11. Step 4: Calculate the variance (^2). The formula for variance is ^2 = ( (x_i - )^2)/(N). First, calculate the deviations from the mean (x_i - ) and their squares (x_i - )^2: • For 8: (8 - 11)^2 = (-3)^2 = 9 • For 9: (9 - 11)^2 = (-2)^2 = 4 • For 11: (11 - 11)^2 = (0)^2 = 0 • For 12: (12 - 11)^2 = (1)^2 = 1 • For 15: (15 - 11)^2 = (4)^2 = 16 Sum of the squared deviations: (x_i - )^2 = 9 + 4 + 0 + 1 + 16 = 30 Now, calculate the variance: ^2 = (30)/(5) = 6 Step 5: Calculate the standard deviation (). The standard deviation is the square root of the variance. = sqrt(^2) = sqrt(6) ≈ 2.449 What's next?