Difference between revisions of "Manuals/calci/SKEW"

Latest revision as of 13:40, 18 June 2018

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

References

Skewness

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''SKEW(n1,n2,…)'''</div><br/>
+<div style="font-size:30px">'''SKEW()'''</div><br/>
-*<math>n1,n2,…</math> are numbers to calculate the skewness.
+*Parameters are any numbers to calculate the skewness.
+**SKEW() returns the skewness of a distribution
 ==Description==
-*This function gives the skewness of a distribution.
+*This function gives the Skewness of a distribution.
 *Skewness is a measure of the degree of asymmetry of a distribution.
-*A distribution(normal ditribution) is symmetry ,it don't have a skewness.
+*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.
+*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.
-*In 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.
+*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 Left Skewed Distribution, its <math>mean<median<mode</math>
-*In a normal  skewed distribution, its mean=median=mode.
+*In a Normal Skewed Distribution, its <math>mean=median=mode</math>
-*In a right skewed distribution, its mode<median<mean.
+*In a Right Skewed Distribution, its <math>mode<median<mean</math>.
-*In <math>SKEW(n1,n2,...), n1</math>  is required.<math>n2,n3,...</math> are optional.
+*In <math>SKEW(), First parameter is required.From the second parameter 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 :<math> Skewness= \frac{3(mean-median)}{s}</math>  OR <math>skewness= \tfrac{\sum (x_i-\bar{x})^3}{(N-1)s^3}</math>  Where:  s is the sample standard deviation, <math>\bar{x}</math> represents a sample mean.
+*The equation for Skewness is defined by :<math> Skewness = \frac{n}{(n-1)(n-2)}\sum \left(\frac{x_i-\bar{x}}{s} \right)^3</math>
+Where, <math>s</math> is the sample standard deviation, <math>\bar{x}</math> represents a sample mean.
 *This function will return the result as error when
-. Any one of the argument is nonnumeric.
+. Any one of the argument is non-numeric.
-. If there are fewer than three data points, or the sample standard deviation is zero.
+. If there are fewer than three data points, or the Sample Standard Deviation is zero.
+==Examples==
+{| class="wikitable"
+|+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
- where
+==Related Videos==
-<div id="6SpaceContent" class="zcontent" align="left"> <font face="Arial, sans-serif"><font size="2">'''SKEW'''</font></font><font face="Arial, sans-serif"><font size="2">(</font></font><font face="Arial, sans-serif"><font size="2">'''n1'''</font></font><font face="Arial, sans-serif"><font size="2">,n2,...)</font></font>
-<font face="Arial, sans-serif"><font size="2">'''Where n1, n2 ...'''</font></font><font face="Arial, sans-serif"><font size="2">   are numbers to calculate the skewness. </font></font>
+{{#ev:youtube|B0xF7UILeKo|280|center|SKEW}}
-</div>
+==See Also==
-----
+*[[Manuals/calci/KURT| KURT]]
-<div id="1SpaceContent" class="zcontent" align="left">  <font face="Arial, sans-serif"><font size="2">It calculates the skewness of a distribution. </font></font></div>
+*[[Manuals/calci/STDEV  | STDEV ]]
-----
+*[[Manuals/calci/STDEVP | STDEVP ]]
-<div id="7SpaceContent" class="zcontent" align="left">
-# <font face="Arial, sans-serif"><font size="2">If the data points are less than three,the function displays NaN.</font></font>
+==References==
-# <font face="Arial, sans-serif"><font size="2">The equation for skewness is: </font></font>
+*[http://en.wikipedia.org/wiki/Skewness Skewness]
-<br /><br />
-</div>
-----
-<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
-SKEW
-</div></div>
+*[[Z_API_Functions | List of Main Z Functions]]
-----
-<div id="8SpaceContent" class="zcontent" align="left">
-<font face="Arial, sans-serif"><font size="2">C1R1=13</font></font>
-<font face="Arial">C2R2=14</font>
-<font face="Arial">C3R3=15</font>
-<font face="Arial">C4R4=12</font>
-<font face="Arial">C5R5=13</font>
-<font face="Arial">C6R6=14</font>
-<font face="Arial">C7R7=9</font>
-<font face="Arial">C8R8=16</font>
-<font face="Arial">C9R9=14</font>
-<font face="Arial">C10R10=17</font>
-<font face="Arial, sans-serif"><font size="2">i.e.SKEW(Column1Row1:Column1Row10)</font></font>
-<font face="Arial, sans-serif"><font size="2">i.e.= SKEW(C1R1:C1R10) is -0.756</font></font>
-</div>
-----
-<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
-----
-<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
-----
-<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
-----
-<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
-----
-<div id="2SpaceContent" class="zcontent" align="left">
-{| id="TABLE3" class="SpreadSheet blue"
-|- class="even"
-| class=" " |
-| class="  " | Column1
-| class="    " | Column2
-| Column3
-| Column4
-|- class="odd"
-| class=" " | Row1
-| class="sshl_f " | 13
-| class="sshl_f" | -0.756
-| class="sshl_f" |
-| class="sshl_f" |
-|- class="even"
-| class="  " | Row2
-| class="sshl_f" | 14
-| class=" SelectTD SelectTD" |
-<div id="2Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
-|
-|
-|- class="odd"
-| Row3
-| class="sshl_f" | 15
-|
-|
-|
-|- class="even"
-| Row4
-| class="sshl_f" | 12
-|
-|
-| class="  " |
-|- class="odd"
-| class=" " | Row5
-| class="sshl_f" | 13
-|
-|
-|
-|- class="even"
-| class="sshl_f" | Row6
-| class="sshl_f" | 14
-| class="sshl_f" |
-| class="sshl_f" |
-| class="sshl_f" |
-|- class="odd"
-| class="sshl_f  " | Row7
-| class="sshl_f" | 9
-| class="sshl_f" |
-| class="sshl_f" |
-| class="sshl_f" |
-|- class="even"
-| class="sshl_f" | Row8
-| class="sshl_f" | 16
-| class="sshl_f" |
-| class="sshl_f" |
-| class="sshl_f" |
-|- class="odd"
-| class="sshl_f" | Row9
-| class="sshl_f" | 14
-| class="sshl_f" |
-| class="sshl_f" |
-| class="sshl_f" |
-|- class="even"
-| class="sshl_f" | Row10
-| class="sshl_f " | 17
-|
-|
-|
-|}
-<div align="left">[[Image:calci1.gif]]</div></div>
+*[[ Z3 |   Z3 home ]]
-----

Difference between revisions of "Manuals/calci/SKEW"

Latest revision as of 13:40, 18 June 2018

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Description

Examples

Related Videos

See Also

References

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