Std-deviation

Calculate standard deviation for file:

63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90

Correct result:

s =  7.656
s₁ =  7.892

Solution:

$n=17 \ \\ \ \\ m=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)/n=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)/17 \doteq \dfrac{ 1299 }{ 17 } \doteq 76.4118 \ \\ \ \\ a_{1}=(63-m)^2=(63-76.4118)^2 \doteq 179.8754 \ \\ a_{2}=a_{1}+(65-m)^2=179.8754+(65-76.4118)^2 \doteq 310.1038 \ \\ a_{3}=a_{2}+(68-m)^2=310.1038+(68-76.4118)^2 \doteq 380.8616 \ \\ a_{4}=a_{3}+(69-m)^2=380.8616+(69-76.4118)^2 \doteq 435.7958 \ \\ a_{5}=a_{4}+(69-m)^2=435.7958+(69-76.4118)^2 \doteq 490.7301 \ \\ a_{6}=a_{5}+(72-m)^2=490.7301+(72-76.4118)^2 \doteq 510.1938 \ \\ a_{7}=a_{6}+(75-m)^2=510.1938+(75-76.4118)^2 \doteq 512.1869 \ \\ a_{8}=a_{7}+(76-m)^2=512.1869+(76-76.4118)^2 \doteq 512.3564 \ \\ a_{9}=a_{8}+(79-m)^2=512.3564+(79-76.4118)^2 \doteq 519.0554 \ \\ a_{10}=a_{9}+(79-m)^2=519.0554+(79-76.4118)^2 \doteq 525.7543 \ \\ a_{11}=a_{10}+(79-m)^2=525.7543+(79-76.4118)^2 \doteq 532.4533 \ \\ a_{12}=a_{11}+(80-m)^2=532.4533+(80-76.4118)^2 \doteq 545.3287 \ \\ a_{13}=a_{12}+(82-m)^2=545.3287+(82-76.4118)^2 \doteq 576.5571 \ \\ a_{14}=a_{13}+(83-m)^2=576.5571+(83-76.4118)^2 \doteq 619.9619 \ \\ a_{15}=a_{14}+(84-m)^2=619.9619+(84-76.4118)^2 \doteq 677.5433 \ \\ a_{16}=a_{15}+(88-m)^2=677.5433+(88-76.4118)^2 \doteq 811.8304 \ \\ a_{17}=a_{16}+(90-m)^2=811.8304+(90-76.4118)^2 \doteq \dfrac{ 16940 }{ 17 } \doteq 996.4706 \ \\ \ \\ s=\sqrt{ a_{17}/n }=\sqrt{ 996.4706/17 }=7.656$

$s_{1}=\sqrt{ a_{17}/(n-1) }=\sqrt{ 996.4706/(17-1) }=7.892$

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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

1 year ago  Like

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