Difference between revisions of "Manuals/calci/SKEW"

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<div style="font-size:30px">'''SKEW(n1,n2,…)'''</div><br/>
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<div style="font-size:30px">'''SKEW()'''</div><br/>
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*<math>n_1,n_2,…</math> are numbers to calculate the skewness.
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*Parameters are any numbers to calculate the skewness.
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**SKEW() returns the skewness of a distribution
  
 
==Description==
 
==Description==
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*This function gives the skewness of a distribution.  
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*This function gives the Skewness of a distribution.  
 
*Skewness is a measure of the degree of asymmetry of a distribution.  
 
*Skewness is a measure of the degree of asymmetry of a distribution.  
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*A distribution(normal ditribution) is symmetry ,it don't have a skewness.  
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*A distribution(normal distribution) is symmetry ,it don't have a Skewness.  
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*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.  
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*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.  
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*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.   
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*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.   
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*In a left skewed distribution ,its mean<median<mode.
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*In a Left Skewed Distribution, its <math>mean<median<mode</math>
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*In a normal  skewed distribution, its mean=median=mode.
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*In a Normal Skewed Distribution, its <math>mean=median=mode</math>
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*In a right skewed distribution, its mode<median<mean.  
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*In a Right Skewed Distribution, its <math>mode<median<mean</math>.  
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*In <math>SKEW(n_1,n_2,...), n_1</math>  is required.<math>n_2,n_3,...</math> are optional.  
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*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.  
 
*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.  
 
*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.  
 
*Suppose the array contains text,logicl values or empty cells, like that values are not considered.  
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*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.  
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*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>
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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  
 
*This function will return the result as error when  
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   1. Any one of the argument is nonnumeric.  
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   1. Any one of the argument is non-numeric.  
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   2. If there are fewer than three data points, or the sample standard deviation is zero.
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   2. If there are fewer than three data points, or the Sample Standard Deviation is zero.
  
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==Examples==
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{| class="wikitable"
 +
|+Spreadsheet
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|-
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! !! A !! B !! C !! D!! E
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|-
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! 1
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| 0 || 4 || -5 ||4 || 1
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|-
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! 2
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| 29 || 9 || 11 || 5 || 2
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|-
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! 3
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| 41  || 11  || 18  ||2 || 3
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|-
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! 4
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| 18 ||10  || 7  ||5 ||5
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|-
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! 5
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| 4 || 5 || 9  ||6 || 6
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|-
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! 6
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| 38 || 9 || 13  || 8 || 11
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|}
  
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==Examples==
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*=SKEW(B1:B5) = -0.4369344921493
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1.Array={4,9,11,10,5}
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*=SKEW(A1:A6) = -0.21921252920
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SKEW(B1:B5)=-0.4369344921493
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*=SKEW(C1:C4) = -0.715957010
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2.Array={0,29,41,18,4,38}
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*=SKEW(D1:D6) = 0
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SKEW(A1:A6)=-0.21921252920
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*=SKEW(E1:E6) = 1.16584702768
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3.Array={-5,11,18,7}
 
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SKEW(C1:C4)=-0.715957010
 
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4.Array={4,5,2,5,6,8}
 
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SKEW(C1:C6)=0
 
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5.Array={1,2,3,5,6,11}
 
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SKEW(A1:A6)=1.16584702768
 
  
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==Related Videos==
  
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{{#ev:youtube|B0xF7UILeKo|280|center|SKEW}}
  
 
==See Also==
 
==See Also==
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*[[Manuals/calci/STDEV  | STDEV ]]
 
*[[Manuals/calci/STDEV  | STDEV ]]
 
*[[Manuals/calci/STDEVP | STDEVP ]]
 
*[[Manuals/calci/STDEVP | STDEVP ]]
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==References==
 
==References==
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*[http://en.wikipedia.org/wiki/Skewness Skewness]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

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
  • In a Normal Skewed Distribution, its
  • In a Right Skewed Distribution, its .
  • In

Where, is the sample standard deviation, 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

References



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