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

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find skewness {{61,5},{64,18},{67,42},{70,27},{73,8}} [ Calculator, Method and examples ]

Solution:
Your problem `->` skewness {{61,5},{64,18},{67,42},{70,27},{73,8}}


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

`=6745/100`

`=67.45`

`x`
`(2)`
`f`
`(3)`
`f*x`
`(4)=(2)xx(3)`
`(x-bar x)`
`(5)`
`f*(x-bar x)^2`
`(6)=(3)xx(5)`
`f*(x-bar x)^3`
`(7)=(5)xx(6)`
`f*(x-bar x)^4`
`(8)=(5)xx(7)`
615 305 `305=5xx61`
`(4)=(2)xx(3)`
 -6.45 `|61-67.45|=-6.45`
`|x - 67.45|`
 208.0125 `208.0125=5xx-6.45xx-6.45`
`(6)=(2)xx(5)`
 -1341.6806 `-1341.6806=208.0125xx-6.45`
`(7)=(2)xx(6)`
 8653.84 `8653.84=-1341.6806xx-6.45`
`(8)=(2)xx(7)`
6418 1152 `1152=18xx64`
`(4)=(2)xx(3)`
 -3.45 `|64-67.45|=-3.45`
`|x - 67.45|`
 214.245 `214.245=18xx-3.45xx-3.45`
`(6)=(2)xx(5)`
 -739.1453 `-739.1453=214.245xx-3.45`
`(7)=(2)xx(6)`
 2550.0511 `2550.0511=-739.1453xx-3.45`
`(8)=(2)xx(7)`
6742 2814 `2814=42xx67`
`(4)=(2)xx(3)`
 -0.45 `|67-67.45|=-0.45`
`|x - 67.45|`
 8.505 `8.505=42xx-0.45xx-0.45`
`(6)=(2)xx(5)`
 -3.8273 `-3.8273=8.505xx-0.45`
`(7)=(2)xx(6)`
 1.7223 `1.7223=-3.8273xx-0.45`
`(8)=(2)xx(7)`
7027 1890 `1890=27xx70`
`(4)=(2)xx(3)`
 2.55 `|70-67.45|=2.55`
`|x - 67.45|`
 175.5675 `175.5675=27xx2.55xx2.55`
`(6)=(2)xx(5)`
 447.6971 `447.6971=175.5675xx2.55`
`(7)=(2)xx(6)`
 1141.6277 `1141.6277=447.6971xx2.55`
`(8)=(2)xx(7)`
738 584 `584=8xx73`
`(4)=(2)xx(3)`
 5.55 `|73-67.45|=5.55`
`|x - 67.45|`
 246.42 `246.42=8xx5.55xx5.55`
`(6)=(2)xx(5)`
 1367.631 `1367.631=246.42xx5.55`
`(7)=(2)xx(6)`
 7590.352 `7590.352=1367.631xx5.55`
`(8)=(2)xx(7)`
---------------------
--`n=100``sum f*x=6745``--`=852.75``=-269.325``=19937.5931`


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

`=sqrt(852.75/99)`

`=sqrt(8.6136)`

`=2.9349`



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

`=-269.325/(99*(2.9349)^3)`

`=-269.325/(99*25.2802)`

`=-0.1076`








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