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 Sample kurtosis {{61,5},{64,18},{67,42},{70,27},{73,8}}

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


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)`
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)`
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)`
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)`
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)`
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)`
------------------
--`n=100``sum f*x=6745``--`=852.75``=-269.325`


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

`=sqrt(852.75/99)`

`=sqrt(8.6136)`

`=2.9349`



Kurtosis `= (sum(x - bar x)^4)/((n-1)*S^4)`

`=19937.5931/(99*(2.9349)^4)`

`=19937.5931/(99*74.1947)`

`=2.7143`








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

Share with your friends
 
Copyright © 2018. All rights reserved. Terms, Privacy