Std-deviation

Calculate the standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90

Correct answer:

s = 7.6561
s₁ = 7.8917

Step-by-step explanation:

n = 17 m = (63 + 65 + 68 + 69 + 69 + 72 + 75 + 76 + 77 + 79 + 79 + 80 + 82 + 83 + 84 + 88 + 90) / n = (63 + 65 + 68 + 69 + 69 + 72 + 75 + 76 + 77 + 79 + 79 + 80 + 82 + 83 + 84 + 88 + 90) / 17 = \frac{1 2 9 9}{1 7} = 76 \frac{7}{1 7} ≐ 76.4118 a_{1} = (63 - m)^{2} = (63 - 76.4118)^{2} ≐ 179.8754 a_{2} = a_{1} + (65 - m)^{2} = 179.8754 + (65 - 76.4118)^{2} ≐ 310.1038 a_{3} = a_{2} + (68 - m)^{2} = 310.1038 + (68 - 76.4118)^{2} ≐ 380.8616 a_{4} = a_{3} + (69 - m)^{2} = 380.8616 + (69 - 76.4118)^{2} ≐ 435.7958 a_{5} = a_{4} + (69 - m)^{2} = 435.7958 + (69 - 76.4118)^{2} ≐ 490.7301 a_{6} = a_{5} + (72 - m)^{2} = 490.7301 + (72 - 76.4118)^{2} ≐ 510.1938 a_{7} = a_{6} + (75 - m)^{2} = 510.1938 + (75 - 76.4118)^{2} ≐ 512.1869 a_{8} = a_{7} + (76 - m)^{2} = 512.1869 + (76 - 76.4118)^{2} ≐ 512.3564 a_{9} = a_{8} + (79 - m)^{2} = 512.3564 + (79 - 76.4118)^{2} ≐ 519.0554 a_{10} = a_{9} + (79 - m)^{2} = 519.0554 + (79 - 76.4118)^{2} ≐ 525.7543 a_{11} = a_{10} + (79 - m)^{2} = 525.7543 + (79 - 76.4118)^{2} ≐ 532.4533 a_{12} = a_{11} + (80 - m)^{2} = 532.4533 + (80 - 76.4118)^{2} ≐ 545.3287 a_{13} = a_{12} + (82 - m)^{2} = 545.3287 + (82 - 76.4118)^{2} ≐ 576.5571 a_{14} = a_{13} + (83 - m)^{2} = 576.5571 + (83 - 76.4118)^{2} ≐ 619.9619 a_{15} = a_{14} + (84 - m)^{2} = 619.9619 + (84 - 76.4118)^{2} ≐ 677.5433 a_{16} = a_{15} + (88 - m)^{2} = 677.5433 + (88 - 76.4118)^{2} ≐ 811.8304 a_{17} = a_{16} + (90 - m)^{2} = 811.8304 + (90 - 76.4118)^{2} = \frac{1 6 9 4 0}{1 7} = 996 \frac{8}{1 7} ≐ 996.4706 s = a_{17} / n = 996.4706 / 17 = 7.6561

s_{1} = a_{17} / (n - 1) = 996.4706 / (17 - 1) = 7.8917

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Showing 1 comment:

Dr Math

See also our standard deviation calculator for this case:

https://www.hackmath.net/en/calculator/standard-deviation?input=63%2C65%2C68%2C69%2C69%2C72%2C75%2C76%2C77%2C79%2C79%2C80%2C82%2C83%2C84%2C88%2C90

Statistical file:
{63, 65, 68, 69, 69, 72, 75, 76, 77, 79, 79, 80, 82, 83, 84, 88, 90}

Standard deviation σ=7.63165870128
Corrected sample standard deviation s=7.86653373101

6 years ago Like