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Line 1: − + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − '''KURT'''(N'''1''',N2,...)+ − + − '''Where N1,N2,.... '''are the arguments to calculate the kurtosis. − − </div> − ---- − <div id="1SpaceContent" class="zcontent" align="left"> − − This function calculates the relative peakedness or flatness of a distribution compared with the normal distribution. − − </div> − ---- − <div id="7SpaceContent" class="zcontent" align="left"> − − · Arguments can be numbers or names, arrays, or references. − − · Logical values and text representations of numbers are calculated. − − · KURT shows the error value, when there are fewer than four data points, or the SD of the sample equals zero. − − Formulas:- − − · Kurtosis is defined as: − − where s is the sample standard deviation. − − </div> − ---- − <div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left"> − − KURT − − </div></div> − ---- − <div id="8SpaceContent" class="zcontent" align="left"> − − {| class="MsoNormalTable" cellspacing="3" − | valign="top" | − <font face="Arial">Lets see an example,</font> − − <font face="Arial">KURT(N1,N2,....)</font> − − <font face="Arial"></font> − − '''<font face="Arial">B</font>''' − − <font face="Arial"></font>8 − − 9 − − 10 − − 4 − − 5 − − 3 − − 10 − − <font face="Arial"><nowiki>=KURT(B2:B8) is -2.0947</nowiki></font> − − <font face="Arial"></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 − | class=" " | Column3 − | class=" " | Column4 − |- class="odd" − | class=" " | Row1 − | class="sshl_f " | 8 − | class="sshl_f" | -2.094675 − | class="sshl_f" | − | class="sshl_f" | − |- class="even" − | class=" " | Row2 − | class="sshl_f " | 9 − | class="SelectTD" | − | class="sshl_f" | − | class="sshl_f" | − |- class="odd" − | Row3 − | class="sshl_f " | 10 − | class="sshl_f" | − | class="sshl_f" | − | class="sshl_f" | − |- class="even" − | Row4 − | class="sshl_f " | 4 − | class="sshl_f" | − | class="sshl_f" | − | class="sshl_f" | − |- class="odd" − | class=" " | Row5 − | class="sshl_f " | 5 − | class="sshl_f" | − | class="sshl_f" | − | class="sshl_f" | − |- class="even" − | class="sshl_f" | Row6 − | class="sshl_f " | 3 − | class="sshl_f " | − | class="sshl_f " | − | class="sshl_f " | − |- class="odd" − | class="sshl_f" | Row7 − | class="sshl_f " | 10 − | class="sshl_f" | − | class="sshl_f" | − | class="sshl_f" | − |} − − <div align="left">[[Image:calci1.gif]]</div></div> − ----
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<div id="6SpaceContent" class="zcontent" align="left">
<div style="font-size:30px">'''KURT(n1,n2,…)'''</div><br/>
*<math>n1</math>,<math>n2</math> are values to calculate kurtosis.
==Description==
*This function gives the value of kurtosis of a given set.
*Kurtosis is the peakedness or flatness of the graph of a frequency distribution 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,possion distribution, Laplace distribution.
*Example for negative kurtosis(platykurtosis) is Bernoulli distribution, Uniform distribution.
*Kurtosis has no units.
*Kurtosis is defined by:
*kurtosis={n(n+1)/(n-1)(n-2)(n-3)*summation[(xi-x(bar)/s]^4}-3(n-1)^2/(n-2)(n-3), wher s is the sample standard deviation.x(bar) is the arithmetic mean.
*In this function argumentsmay 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 nonnumeric.
#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
==See Also==
*[[Manuals/calci/SKEW | SKEW ]]
*[[Manuals/calci/STDEV | STDEV ]]
*[[Manuals/calci/STDEVP | STDEVP ]]
==References==
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Correlation]