Difference between revisions of "Manuals/calci/KURT"
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*Kurtosis has no units. | *Kurtosis has no units. | ||
*Kurtosis is defined by: | *Kurtosis is defined by: | ||
| − | *Kurtosis={n(n+1) | + | *Kurtosis=: |
| + | <math>{\frac{n(n+1)}{(n-1)(n-2)(n-3)}*\sum[(xi-\bar{x})/s]^4}-3(n-1)^2/(n-2)(n-3)</math>, where <math>s</math> is the sample standard deviation.x(bar) is the arithmetic mean. | ||
*In this function arguments may be any type like numbers,names,arrays or references that contain numbers. | *In this function arguments may be any type like numbers,names,arrays or references that contain numbers. | ||
*We can give logical values and text references also directly. | *We can give logical values and text references also directly. | ||
*Suppose the referred argument contains any null cells, logical values like that values are not considered. | *Suppose the referred argument contains any null cells, logical values like that values are not considered. | ||
*This function will return the result as error when | *This function will return the result as error when | ||
| − | #Any one of the argument is | + | #Any one of the argument is non-numeric. |
#suppose the number of data points are less than four or the standard deviation of the sampleis zero | #suppose the number of data points are less than four or the standard deviation of the sampleis zero | ||
#The referred arguments could not convert | #The referred arguments could not convert | ||
Revision as of 01:59, 13 December 2013
KURT(n1,n2,…)
- , are values to calculate kurtosis.
,
are values to calculate kurtosis.Description
- This function gives the value of Kurtosis of a given set.
- Kurtosis is the peak or flatness of a frequency distribution graph especially with respect to the concentration of values near the Mean as compared with the Normal Distribution.
- A normal distribution has a Kurtosis of 3.
- Distributions having higher Kurtosis have flatter tails or more extreme values that phenomenon called 'leptokurtosis' also it is the positive excess Kurtosis , and those with lower Kurtosis have fatter middles or fewer extreme value that phenomenon called 'Platykurtosis' also it is the negative excess Kurtosis.
- Example for positive Kurtosis(leptokurtosis) is Exponential distribution, Poisson distribution, Laplace Distribution.
- Example for Negative Kurtosis(platykurtosis) is Bernoulli distribution, Uniform distribution.
- Kurtosis has no units.
- Kurtosis is defined by:
- Kurtosis=:
, where is the sample standard deviation.x(bar) is the arithmetic mean.
![{\displaystyle {{\frac {n(n+1)}{(n-1)(n-2)(n-3)}}*\sum [(xi-{\bar {x}})/s]^{4}}-3(n-1)^{2}/(n-2)(n-3)}](https://wikimedia.org/api/rest_v1/media/math/render/png/1d4ba89e77f5f25a85ca9769172db005bc04108e)
, where 
is the sample standard deviation.x(bar) is the arithmetic mean.
- In this function arguments may be any type like numbers,names,arrays or references that contain numbers.
- We can give logical values and text references also directly.
- Suppose the referred argument contains any null cells, logical values like that values are not considered.
- This function will return the result as error when
- Any one of the argument is non-numeric.
- suppose the number of data points are less than four or the standard deviation of the sampleis zero
- The referred arguments could not convert
in to numbers.
Examples
1.DATA 14 11 23 54 38 KURT(C1:C5)=-0.8704870492 2. DATA={6,7,8,9,10} KURT(A1:A5)=-1.199999999 3.DATA={1898,1987,1786,1947} KURT(B1:B4)=0.870901113729 4.DATA={26,16,12} KURT(D1:D3)=NAN