Home > Statistical Methods calculators > Sample Skewness, Kurtosis for ungrouped data calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find Sample skewness {85,96,76,108,85,80,100,85,70,95} [ Calculator, Method and examples ]

Solution:
Your problem `->` Sample skewness {85,96,76,108,85,80,100,85,70,95}


Skewness :
Mean `bar x = (sum x)/n`

`=(85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10`

`=880/10`

`=88`

`x``(x - bar x)`
`= (x - 88)`
`(x - bar x)^2`
`= (x - 88)^2`
`(x - bar x)^3`
`= (x - 88)^3`
`(x - bar x)^4`
`= (x - 88)^4`
85 -3 `(85-88)=-3`
`(x - 88)`
 9 `(85-88)^2=9`
`(x - 88)^2`
 -27 `(85-88)^3=-27`
`(x - 88)^3`
 81 `(85-88)^4=81`
`(x - 88)^4`
96 8 `(96-88)=8`
`(x - 88)`
 64 `(96-88)^2=64`
`(x - 88)^2`
 512 `(96-88)^3=512`
`(x - 88)^3`
 4096 `(96-88)^4=4096`
`(x - 88)^4`
76 -12 `(76-88)=-12`
`(x - 88)`
 144 `(76-88)^2=144`
`(x - 88)^2`
 -1728 `(76-88)^3=-1728`
`(x - 88)^3`
 20736 `(76-88)^4=20736`
`(x - 88)^4`
108 20 `(108-88)=20`
`(x - 88)`
 400 `(108-88)^2=400`
`(x - 88)^2`
 8000 `(108-88)^3=8000`
`(x - 88)^3`
 160000 `(108-88)^4=160000`
`(x - 88)^4`
85 -3 `(85-88)=-3`
`(x - 88)`
 9 `(85-88)^2=9`
`(x - 88)^2`
 -27 `(85-88)^3=-27`
`(x - 88)^3`
 81 `(85-88)^4=81`
`(x - 88)^4`
80 -8 `(80-88)=-8`
`(x - 88)`
 64 `(80-88)^2=64`
`(x - 88)^2`
 -512 `(80-88)^3=-512`
`(x - 88)^3`
 4096 `(80-88)^4=4096`
`(x - 88)^4`
100 12 `(100-88)=12`
`(x - 88)`
 144 `(100-88)^2=144`
`(x - 88)^2`
 1728 `(100-88)^3=1728`
`(x - 88)^3`
 20736 `(100-88)^4=20736`
`(x - 88)^4`
85 -3 `(85-88)=-3`
`(x - 88)`
 9 `(85-88)^2=9`
`(x - 88)^2`
 -27 `(85-88)^3=-27`
`(x - 88)^3`
 81 `(85-88)^4=81`
`(x - 88)^4`
70 -18 `(70-88)=-18`
`(x - 88)`
 324 `(70-88)^2=324`
`(x - 88)^2`
 -5832 `(70-88)^3=-5832`
`(x - 88)^3`
 104976 `(70-88)^4=104976`
`(x - 88)^4`
95 7 `(95-88)=7`
`(x - 88)`
 49 `(95-88)^2=49`
`(x - 88)^2`
 343 `(95-88)^3=343`
`(x - 88)^3`
 2401 `(95-88)^4=2401`
`(x - 88)^4`
---------------
880012162430317284


Sample Standard deviation `S = sqrt((sum (x - bar x)^2)/(n-1))`

`=sqrt(1216/9)`

`=sqrt(135.1111)`

`=11.6237`



Sample Skewness `= (sum(x - bar x)^3)/((n-1)*S^3)`

`=2430/(9*(11.6237)^3)`

`=2430/(9*1570.4951)`

`=0.1719`








Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

 
Copyright © 2019. All rights reserved. Terms, Privacy





We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more