|
Statistics[Mean] - compute the arithmetic mean
|
|
Calling Sequence
|
|
Mean(A, ds_options)
Mean(M, ds_options)
Mean(X, rv_options)
|
|
|
Parameters
|
|
|
A
|
-
|
Array; data sample
|
|
M
|
-
|
Matrix data set
|
|
X
|
-
|
algebraic; random variable or distribution
|
|
ds_options
|
-
|
(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the mean of a data set
|
|
rv_options
|
-
|
(optional) equation of the form numeric=value; specifies options for computing the mean of a random variable
|
|
|
|
|
|
Description
|
|
|
•
|
The Mean function computes the arithmetic mean of the specified random variable or data set.
|
|
|
|
Computation
|
|
|
•
|
By default, all computations involving random variables are performed symbolically (see option numeric below).
|
|
•
|
All computations involving data are performed in floating-point; therefore, all data provided must have type[realcons] and all returned solutions are floating-point, even if the problem is specified with exact values.
|
|
|
|
Data Set Options
|
|
|
|
The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.
|
|
•
|
ignore=truefalse -- This option controls how missing data is handled by the Mean command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Mean command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.
|
|
•
|
weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight  .
|
|
|
|
Random Variable Options
|
|
|
|
The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
|
|
•
|
numeric=truefalse -- By default, the mean is computed using exact arithmetic. To compute the mean numerically, specify the numeric or numeric = true option.
|
|
|
|
Compatibility
|
|
|
•
|
The M parameter was introduced in Maple 16.
|
|
|
|
Examples
|
|
|
>
|
|
Compute the mean of the beta distribution with parameters p and q.
|
>
|
|
|
| (1) |
Use numeric parameters.
|
>
|
|
|
| (2) |
|
>
|
|
|
| (3) |
Generate a random sample of size 100000 drawn from the above distribution and compute the sample mean.
|
>
|
|
|
>
|
|
|
| (4) |
Compute the standard error of the sample mean for the normal distribution with parameters 5 and 2.
|
>
|
|
|
| (5) |
|
>
|
|
|
>
|
]](/support/helpjp/helpview.aspx?si=4678/file02894/math273.png)
|
|
![[5, 1/500]](/support/helpjp/helpview.aspx?si=4678/file02894/math276.png)
| (6) |
|
>
|
|
|
| (7) |
Create a beta-distributed random variable  and compute the mean of  .
|
>
|
|
|
>
|
|
|
| (8) |
|
>
|
|
|
| (9) |
Verify this using simulation.
|
>
|
|
|
>
|
|
|
| (10) |
Compute the mean of a weighted data set.
|
>
|
|
|
>
|
|
|
>
|
|
|
| (11) |
|
>
|
|
|
| (12) |
Consider the following Matrix data set.
|
>
|
![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4678/file02894/math353.png)
|
|
![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4678/file02894/math356.png)
| (13) |
We compute the mean of each of the columns.
|
>
|
|
|
](/support/helpjp/helpview.aspx?si=4678/file02894/math365.png)
| (14) |
|
|
|
References
|
|
|
|
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
|
|
|
Download Help Document
Was this information helpful?
