# 2.13.1.11 mmoments(Pro)

## Brief Information

Compute moments on matrix data

This feature is for OriginPro only.

## Command Line Usage

 

1. mmoments im:=MBook1; 

2. mmoments im:=MBook1 mean:=mymean; 

## Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Input Matrix im

Input

MatrixObject

<active>

Specifies the input data range

Mean mean

Output

double

<unassigned>

The variable specifies the output for the arithmetic average.

Standard Deviation sd

Output

double

<unassigned>

The variable specifies the output for the standard deviation, which is a statistical measure of the distance a quantity is likely to lie from the average value of a group of data.

SE of Mean se

Output

double

<unassigned>

The variable specifies the output for the standard error of the mean, which is used to estimate the deviation of the population mean.

Number of Observations n

Output

int

<unassigned>

The variable specifies the output for the number of valid observations

Sum sum

Output

double

<unassigned>

The variable specifies the output for the arithmetic sum of selected dataset

Skewness skewness

Output

double

<unassigned>

The variable specifies the output for skewness, which reveals the symmetry of sample distribution. A positive skewness implies the distribution curve skew to right while a negative value indicates the curve skew to left

Kurtosis kurtosis

Output

double

<unassigned>

The variable specifies the output for kurtosis, which indicates how flat or peaked a distribution is. Negative values correspond to flat distributions, while positive values correspond to peaked distributions.

Coefficient of Variation cv

Output

double

<unassigned>

The variable specifies the coefficient of variation, which gives a measure of how dispersed a dataset is. This measure can be used to compare distributions of different sizes and with different means.

## Description

The "moments" command displays the mean, standard deviation, and other summary statistics of a given dataset. moments are used to describe certain basic features of the data in a study.

The X-function of mmoments is used to compute the summary statistics of a Matrix object. It can give out the mean, standard deviation, standard error, kurtosis, skewness, and coefficient of variation of the specified Matrix.

## Examples

1. List all input and output results of descriptive statistics of given Matrix
mmoments im:=MBook1;

2. To return the standard deviation of given Matrix from the Command Window, type the following:
mmoments im:=MBook1 sd:=mysd; mysd=

## Algorithm

Let for denotes the input value, then:

1. Mean is computed using the following equation:

2. Standard deviation is computed as follows:

3. Standard error is computed as:

4. Sample size is the total number of valid values in a data set

5. Sum is computed using following equation:

6. Skewness is computed as:

7. Kurtosis is computed as:

8. Coefficient of variance is computed as:

## References

Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall.