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:

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=129917≐76.4118  a1=(63−m)2=(63−76.4118)2≐179.8754 a2=a1+(65−m)2=179.8754+(65−76.4118)2≐310.1038 a3=a2+(68−m)2=310.1038+(68−76.4118)2≐380.8616 a4=a3+(69−m)2=380.8616+(69−76.4118)2≐435.7958 a5=a4+(69−m)2=435.7958+(69−76.4118)2≐490.7301 a6=a5+(72−m)2=490.7301+(72−76.4118)2≐510.1938 a7=a6+(75−m)2=510.1938+(75−76.4118)2≐512.1869 a8=a7+(76−m)2=512.1869+(76−76.4118)2≐512.3564 a9=a8+(79−m)2=512.3564+(79−76.4118)2≐519.0554 a10=a9+(79−m)2=519.0554+(79−76.4118)2≐525.7543 a11=a10+(79−m)2=525.7543+(79−76.4118)2≐532.4533 a12=a11+(80−m)2=532.4533+(80−76.4118)2≐545.3287 a13=a12+(82−m)2=545.3287+(82−76.4118)2≐576.5571 a14=a13+(83−m)2=576.5571+(83−76.4118)2≐619.9619 a15=a14+(84−m)2=619.9619+(84−76.4118)2≐677.5433 a16=a15+(88−m)2=677.5433+(88−76.4118)2≐811.8304 a17=a16+(90−m)2=811.8304+(90−76.4118)2=1694017≐996.4706  s=a17/n=996.4706/17=7.6561
s1=a17/(n−1)=996.4706/(17−1)=7.8917

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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

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