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 2: Calculate the Range (continued from previous response) The minimum value in the dataset is 2.62. The maximum value in the dataset is 3.57. The range is the difference between the maximum and minimum values: Range = Max - Min = 3.57 - 2.62 = 0.95 The range is 0.95. Step 3: Calculate the Standard Deviation (s) The formula for the sample standard deviation is: s = sqrt( (x_i - x))^2n-1 We have n=7 and x ≈ 3.065714. First, calculate the difference between each data point and the mean (x_i - x) and square it (x_i - x)^2: • 2.75 - 3.065714 = -0.315714 (-0.315714)^2 ≈ 0.099675 • 2.86 - 3.065714 = -0.205714 (-0.205714)^2 ≈ 0.042318 • 3.57 - 3.065714 = 0.504286 (0.504286)^2 ≈ 0.254304 • 2.62 - 3.065714 = -0.445714 (-0.445714)^2 ≈ 0.198661 • 3.49 - 3.065714 = 0.424286 (0.424286)^2 ≈ 0.180018 • 3.05 - 3.065714 = -0.015714 (-0.015714)^2 ≈ 0.000247 • 3.12 - 3.065714 = 0.054286 (0.054286)^2 ≈ 0.002947 Next, sum the squared differences: (x_i - x)^2 ≈ 0.099675 + 0.042318 + 0.254304 + 0.198661 + 0.180018 + 0.000247 + 0.002947 ≈ 0.77817 Now, substitute this sum into the standard deviation formula: s = sqrt((0.77817)/(7-1)) s = sqrt((0.77817)/(6)) s = sqrt(0.129695) s ≈ 0.3601319 Rounding to three decimal places: s ≈ 0.360 The standard deviation is 0.360.