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

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find Population skewness {85,96,76,108,85,80,100,85,70,95}

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


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


Population Standard deviation `sigma = sqrt((sum (x - bar x)^2)/n)`

`=sqrt(1216/10)`

`=sqrt(121.6)`

`=11.0272`



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

`=2430/(10*(11.0272)^3)`

`=2430/(10*1340.9123)`

`=0.1812`








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, if solutions are helpful to you.
 
Copyright © 2019. All rights reserved. Terms, Privacy