 NCL Home > Documentation > Functions > General applied math, Statistics

# dim_variance

Computes the unbiased estimates of the variance of a variable's rightmost dimension.

## Prototype

```	function dim_variance (
x  : numeric
)

return_val  :  float or double
```

## Arguments

x

A variable of numeric type and any dimensionality.

## Return value

The output will be double if x is double, and float otherwise.

The output dimensionality is the same as the first n-2 dimensions of the input variable. That is, the dimension rank of the input variable will be reduced by one.

## Description

The dim_variance function computes the unbiased estimate of the variance of all elements of the n-1 dimension for each index of the dimensions 0...n-2. Missing values are ignored.

Technically, this function calculates an estimate of the sample variance. This means that it divides by [1/(N-1)] where N is the total number of non-missing values.

Use dim_variance_n if you want to specify which dimension(s) to calculate the variance.

Use the dim_variance_Wrap function if metadata retention is desired. The interface is identical.

## Examples

Example 1

The following calculates the population and sample variance of 5 values. For illustration, a step-by-step calculation of the variance is done. The variances returned by NCL's three built-in variance functions are included. All return the sample variance.

```  f      = (/ 7, 9, -2, -8, 2/)

favg   = avg(f)             ; average
fdev   = f-favg             ; deviations
fdev2  = fdev^2             ; deviations squared
nf     = dimsizes(f)        ; N

pvar   = sum(fdev2)/nf      ; population variance

svar   = sum(fdev2)/(nf-1)  ; sample variance
var1   = variance(f)
var2   = dim_variance(f)

; Use dim_variance_Wrap if metadata retention is desired
; var2   = dim_variance_Wrap(f)

var3   = dim_variance_n(f,0)

; Use dim_variance_n_Wrap if metadata retention is desired
; var3   = dim_variance_n_Wrap(f,0)

print("pvar="+pvar+"  svar="+svar+"  var1="+var1+"  var2="+var2+"  var3="+var3)

===
output:   pvar=37.84  svar=47.3  var1=47.3  var2=47.3  var3=47.3

```

Example 2

Create a variable q of size (3,5,10) array. Then calculate the sample variance of the rightmost dimension.

```    q   = random_uniform(-20,100,(/3,5,10/))
qVar= dim_variance(q)   ;==>  qVar(3,5)

; Use dim_variance_Wrap if metadata retention is desired
; qVar= dim_variance_Wrap(q)   ;==>  qVar(3,5)
```
Example 3

Let x be of size (ntim,nlat,mlon) and with named dimensions "time", "lat" and "lon", respectively. Then, for each time and latitude, the the variance is:

```    xVarLon= dim_variance( x )    ; ==> xVarLon(ntim,nlat)

; Use dim_variance_Wrap if metadata retention is desired
; xVarLon = dim_variance_Wrap( x )    ; ==> xVarLon(time,lat)
```
Example 4

Let x be defined as in Example 3: x(time,lat,lon). Compute the temporal variance at each latitude/longitude grid point. Use NCL's named subscripting to reorder the input array such that "time" is the rightmost dimension.

Note: Use dim_variance_n to avoid having to reorder your data.

```    xVarTime = dim_variance( x(lat|:, lon|:, time|:) )    ; ==> xVarTime(nlat,nlon)

; Use dim_variance_Wrap if metadata retention is desired
; xVarTime = dim_variance_Wrap( \
;            x(lat|:, lon|:, time|:) )    ; ==> xVarTime(lat,lon)

xVarTime = dim_variance_n(x, 0)                       ; no reordering needed

; Use dim_variance_n_Wrap if metadata retention is desired
; xVarTime = dim_variance_n_Wrap(x,0) ; no reordering needed
```