Manuals/calci/SKEW

SKEW()

• Parameters are any numbers to calculate the skewness.
  • SKEW() returns the skewness of a distribution

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 $SKEW(),Firstparameterisrequired.Fromthesecondparameterareoptional.*Incalcithereisnorestrictionforgivingthenumberofarguments.*Theargumentscanbebeeithernumbersornames,array,constantsorreferencesthatcontainnumbers.*Supposethearraycontainstext,logiclvaluesoremptycells,likethatvaluesarenotconsidered.*TheequationforSkewnessisdefinedby:<math>Skewness={\frac {n}{(n-1)(n-2)}}\sum \left({\frac {x_{i}-{\bar {x}}}{s}}\right)^{3}$

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	4	1
2	29	9	11	5	2
3	41	11	18	2	3
4	18	10	7	5	5
5	4	5	9	6	6
6	38	9	13	8	11

• =SKEW(B1:B5) = -0.4369344921493
• =SKEW(A1:A6) = -0.21921252920
• =SKEW(C1:C4) = -0.715957010
• =SKEW(D1:D6) = 0
• =SKEW(E1:E6) = 1.16584702768

Related Videos

SKEW

See Also

• KURT
• STDEV
• STDEVP

References

• Skewness

• List of Main Z Functions

• Z3 home