Manuals/calci/SKEW

SKEW(n1,n2,…)

• Failed to parse (syntax error): {\displaystyle n_1,n_2,…} are numbers to calculate the skewness.

Description

• This function gives the Skewness of a distribution.
• Skewness is a measure of the degree of asymmetry of a distribution.
• A distribution(normal distribution) is symmetry ,it don't have a Skewness.
• In a distribution the left tail is more pronounced than the right tail (towards more negative values) then the function is said to have Negative Skewness.
• If a distribution is skewed to the right, the tail on the curve's right-hand side is longer than the tail on the left-hand side (towards more positive values), then the function is said to have a positive skewness.
• In a Left Skewed Distribution, its $mean<median<mode$
• In a Normal Skewed Distribution, its $mean=median=mode$
• In a Right Skewed Distribution, its $mode<median<mean$.
• In $SKEW(n_{1},n_{2},...),n_{1}$ is required.$n_{2},n_{3},...$ are optional.
• In calci there is no restriction for giving the number of arguments.
• The arguments can be be either numbers or names, array,constants or references that contain numbers.
• Suppose the array contains text,logicl values or empty cells, like that values are not considered.
• The equation for Skewness is defined by :$Skewness={\frac {n}{(n-1)(n-2)}}\sum \left({\frac {x_{i}-{\bar {x}}}{s}}\right)^{3}$

Where, $s$ is the sample standard deviation, ${\bar {x}}$ represents a sample mean.

• This function will return the result as error when

 1. Any one of the argument is non-numeric. 
 2. If there are fewer than three data points, or the Sample Standard Deviation is zero.

Examples

Spreadsheet

	A	B	C	D	E
1	0	4	-5	9	1
2	29	9	11	20	2
3	41	11	18	6	3
4	18	10	7	42	5
5	4	5	9	78	6
6	38	9	13	48	11

1.Array={4,9,11,10,5} =SKEW(B1:B5)=-0.4369344921493 2.Array={0,29,41,18,4,38} =SKEW(A1:A6)=-0.21921252920 3.Array={-5,11,18,7} =SKEW(C1:C4)=-0.715957010 4.Array={4,5,2,5,6,8} =SKEW(C1:C6)=0 5.Array={1,2,3,5,6,11} =SKEW(E1:E6)=1.16584702768

See Also

• KURT
• STDEV
• STDEVP