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: Calculate the mean (x) of the numbers. The given numbers are 4, 6, 8, 10, 12. There are n=5 numbers. x = ( x)/(n) = (4 + 6 + 8 + 10 + 12)/(5) = (40)/(5) = 8 Step 2: Calculate the sum of the squared differences from the mean, (x - x)^2. (4 - 8)^2 &= (-4)^2 = 16 \\ (6 - 8)^2 &= (-2)^2 = 4 \\ (8 - 8)^2 &= (0)^2 = 0 \\ (10 - 8)^2 &= (2)^2 = 4 \\ (12 - 8)^2 &= (4)^2 = 16 (x - x)^2 = 16 + 4 + 0 + 4 + 16 = 40 Step 3: Calculate the variance (^2). ^2 = (x - x)^2n = (40)/(5) = 8 The variance is 8. Step 4: Calculate the standard deviation (). The standard deviation is the square root of the variance. = sqrt(^2) = sqrt(8) = sqrt(4 × 2) = 2sqrt(2) ≈ 2.83 The standard deviation is 2sqrt(2). Send me the next one 📸