Sample Skewness, Kurtosis for ungrouped data calculator

SolutionHelp

1. 85,96,76,108,85,80,100,85,70,95

2. 3,13,11,11,5,4,2

3. 3,23,13,11,15,3,5,4,2

4. 69,66,67,69,64,63,65,68,72

5. 4,14,12,16,6,3,1,2,3

6. 73,70,71,73,68,67,69,72,76,71

7. 10,50,30,20,10,20,70,30

Example

1. Calculate Sample Skewness from the following data
$85,96,76,108,85,80,100,85,70,95$

Solution:
Skewness :
Mean

$bar x=(sum x)/n$

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

$=880/10$

$=88$

Sample Standard deviation

$S = sqrt((sum (x - bar x)^2)/(n-1))$

$=sqrt(1216/9)$

$=sqrt(135.1111)$

$=11.6237$

Sample Skewness

$= (sum(x - bar x)^3)/((n-1)*S^3)$

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

$=2430/(9*1570.4951)$

$=0.1719$