# Manuals/calci/KURT

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**KURT()**

- Parameters are any values to calculate kurtosis.
- KURT(), returns the kurtosis of a data set.

## 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. 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

1.Any one of the argument is non-numeric. 2.Suppose the number of data points are less than four or the standard deviation of the sample is zero 3.The referred arguments could not convert in to numbers.

- When calculating kurtosis, a result of +3.00 indicates the absence of kurtosis (distribution is mesokurtic).
- For simplicity in its interpretation, some statisticians adjust this result to zero (i.e. kurtosis minus 3 equals zero), and then any reading other than zero is referred to as excess kurtosis.
- Negative numbers indicate a platykurtic distribution and positive numbers indicate a leptokurtic distribution.
- The below table is listing the Kurtosis excess for the number of common distributions:

Distribution | Kurtosis excess |
---|---|

Bernoulli distribution | |

Beta distribution | |

Binomial distribution | |

Chi squared distribution | |

Exponential distribution | 6 |

Gamma distribution | |

Log normal distribution | |

Negative binomial distribution | |

Normal distribution | 0 |

Poisson distribution | |

Student's t distribution |

## ZOS

- The syntax is to calculate KURTOSIS in ZOS is
- Parameters are any values to calculate kurtosis.

- For e.g., KURT([-1..-10,20..25..0.5])

## Examples

A | B | C | D | E | |
---|---|---|---|---|---|

1 | 14 | 11 | 23 | 54 | 38 |

2 | 6 | 7 | 8 | 9 | 10 |

3 | 1898 | 1987 | 1786 | 1947 | |

4 | 26 | 16 | 12 |

- =KURT(A1:E1) = -0.8704870491886512
- =KURT(A2:E2) = -1.199999999
- =KURT(A3:D3) = 0.8709011137293157
- =KURT(A4:C4) = NAN

## Related Videos

## See Also

## References