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
Here are the calculations for the given data: 2, 4, 3, 5, 1, 4, 3, 2. The number of observations is n = 8. Step 1: Calculate the sample mean (x). The formula for the sample mean is x = ( x_i)/(n). x_i = 2 + 4 + 3 + 5 + 1 + 4 + 3 + 2 = 24 x = (24)/(8) = 3 The sample mean is 3. Step 2: Calculate the mean deviation (MD). The formula for the mean deviation is MD = |x_i - x|n. First, find the absolute differences from the mean: |2 - 3| = 1 |4 - 3| = 1 |3 - 3| = 0 |5 - 3| = 2 |1 - 3| = 2 |4 - 3| = 1 |3 - 3| = 0 |2 - 3| = 1 |x_i - x| = 1 + 1 + 0 + 2 + 2 + 1 + 0 + 1 = 8 MD = (8)/(8) = 1 The mean deviation is 1. Step 3: Calculate the sample variance (s^2). The formula for the sample variance is s^2 = (x_i - x)^2n-1. First, find the squared differences from the mean: (2 - 3)^2 = (-1)^2 = 1 (4 - 3)^2 = (1)^2 = 1 (3 - 3)^2 = (0)^2 = 0 (5 - 3)^2 = (2)^2 = 4 (1 - 3)^2 = (-2)^2 = 4 (4 - 3)^2 = (1)^2 = 1 (3 - 3)^2 = (0)^2 = 0 (2 - 3)^2 = (-1)^2 = 1 (x_i - x)^2 = 1 + 1 + 0 + 4 + 4 + 1 + 0 + 1 = 12 s^2 = (12)/(8-1) = (12)/(7) ≈ 1.714 The sample variance is (12)/(7) ≈ 1.714. Step 4: Calculate the sample standard deviation (s). The formula for the sample standard deviation is s = sqrt(s^2). s = sqrt((12)/(7)) ≈ sqrt(1.7142857) ≈ 1.309 The sample standard deviation is sqrt((12)/(7)) ≈ 1.309. Send me the next one 📸