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 =  7.6561
s₁ =  7.8917

Solution:

$$\begin{gathered} n=17 \\ m=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)\mathrm{/}n=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)\mathrm{/}17={\displaystyle \frac{1299}{17}}\doteq 76.4118 \\ {a}_1=(63-m{)}^2=(63-76.4118{)}^2\doteq 179.8754 \\ {a}_2=a_1+(65-m{)}^2=179.8754+(65-76.4118{)}^2\doteq 310.1038 \\ {a}_3=a_2+(68-m{)}^2=310.1038+(68-76.4118{)}^2\doteq 380.8616 \\ {a}_4=a_3+(69-m{)}^2=380.8616+(69-76.4118{)}^2\doteq 435.7958 \\ {a}_5=a_4+(69-m{)}^2=435.7958+(69-76.4118{)}^2\doteq 490.7301 \\ {a}_6=a_5+(72-m{)}^2=490.7301+(72-76.4118{)}^2\doteq 510.1938 \\ {a}_7=a_6+(75-m{)}^2=510.1938+(75-76.4118{)}^2\doteq 512.1869 \\ {a}_8=a_7+(76-m{)}^2=512.1869+(76-76.4118{)}^2\doteq 512.3564 \\ {a}_9=a_8+(79-m{)}^2=512.3564+(79-76.4118{)}^2\doteq 519.0554 \\ {a}_{10}=a_9+(79-m{)}^2=519.0554+(79-76.4118{)}^2\doteq 525.7543 \\ {a}_{11}=a_{10}+(79-m{)}^2=525.7543+(79-76.4118{)}^2\doteq 532.4533 \\ {a}_{12}=a_{11}+(80-m{)}^2=532.4533+(80-76.4118{)}^2\doteq 545.3287 \\ {a}_{13}=a_{12}+(82-m{)}^2=545.3287+(82-76.4118{)}^2\doteq 576.5571 \\ {a}_{14}=a_{13}+(83-m{)}^2=576.5571+(83-76.4118{)}^2\doteq 619.9619 \\ {a}_{15}=a_{14}+(84-m{)}^2=619.9619+(84-76.4118{)}^2\doteq 677.5433 \\ {a}_{16}=a_{15}+(88-m{)}^2=677.5433+(88-76.4118{)}^2\doteq 811.8304 \\ {a}_{17}=a_{16}+(90-m{)}^2=811.8304+(90-76.4118{)}^2={\displaystyle \frac{16940}{17}}\doteq 996.4706 \\ s=\sqrt{a_{17}\mathrm{/}n}=\sqrt{996.4706\mathrm{/}17}=7.6561 \end{gathered}$$

$s_1=\sqrt{a_{17}\mathrm{/}(n-1)}=\sqrt{996.4706\mathrm{/}(17-1)}=7.8917$

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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

1 year ago  Like

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