# GUIskewness

GUIskewness shows the necessary calculations to obtain the variance in a GUI.

## Syntax

• out=GUIskewness(x)example
• out=GUIskewness(x, flag)example
• out=GUIskewness(x, flag, w)example

## Description

 out =GUIskewness(x) Calculation of biased index of skewness.

 out =GUIskewness(x, flag) Calculation of unbiased index of skewness.

 out =GUIskewness(x, flag, w) Calculation of weighted unbiased index of skewness.

## Examples

expand all

### Calculation of biased index of skewness.

Vector x contains the expenditure of 20 customers in a supermarket. (See page 178 of [MRZ])

x=[20, 110,  31, 125,  40, 128,  50, 140,  65, 150,  72, 175,...
85, 190,  100, 205,  100, 230,  105 310];
GUIskewness(x)
ans =

struct with fields:

data: [21×5 table]
gamma: 0.8254



### Calculation of unbiased index of skewness.

Vector x contains the expenditure of 20 customers in a supermarket. (See page 178 of [MRZ])

x=[20, 110,  31, 125,  40, 128,  50, 140,  65, 150,  72, 175,...
85, 190,  100, 205,  100, 230,  105 310];
GUIskewness(x,0)

### Calculation of weighted unbiased index of skewness.

Italian grades obtained in a particular university exam by 1000 students. (See page 54 of [CMR])

x=20:29;
% w= vector of frequencies
w=[61    82   102   164   122   122    61   143    82    61];
GUIskewness(x,0,w)

## Related Examples

expand all

### Calculation of weighted biased index of skewness.

Italian grades obtained in a particular university exam by 1000 students. (See page 54 of [CMR])

x=20:29;
% w= vector of frequencies
w=[61    82   102   164   122   122    61   143    82    61];
GUIskewness(x,1,w)

## Input Arguments

### x — vector of numeric data. Vector.

Vector containing strictly numerical data.

Data Types: double

### flag — flag for unbiasness. Scalar.

If flag=0 the unbiased index is computed.

If flag=1 (default) the biased index is computed, meaning that it tends to differ from the population skewness by a systematic amount based on the sample size.

Example: 1 

Data Types: double

### w — weights. Vector.

Vector of the same length of x containing the weights assigned to each observation.

Example: 1:10 

Data Types: double

## Output Arguments

### out —detailed output to compute the index. Table

Table with n+1 rows (where n is the length of x) containing what is shown in the GUI. Last row contains the totals.

## References

Milioli, M.A., Riani, M., Zani, S. (2019), "Introduzione all'analisi dei dati statistici (Quarta edizione ampliata)". [MRZ]

Cerioli, A., Milioli, M.A., Riani, M. (2016), "Esercizi di statistica (Quinta edizione)". [CMR]

## See Also

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