# meanm

Mean location of geographic coordinates

## Syntax

```[latmean,lonmean] = meanm(lat,lon) [latmean,lonmean] = meanm(lat,lon,units) [latmean,lonmean] = meanm(lat,lon,ellipsoid) ```

## Description

`[latmean,lonmean] = meanm(lat,lon)` returns row vectors of the geographic mean positions of the columns of the input latitude and longitude points.

`[latmean,lonmean] = meanm(lat,lon,units)` indicates the angular units of the data. The default angle unit is `'degrees'`.

`[latmean,lonmean] = meanm(lat,lon,ellipsoid)` specifies the shape of the Earth using `ellipsoid`, which can be a `referenceSphere`, `referenceEllipsoid`, or `oblateSpheroid` object, or a vector of the form ```[semimajor_axis eccentricity]```. The default ellipsoid model is a spherical Earth, which is sufficient for most applications.

If a single output argument is used, then ```geomeans = [latmean,longmean]```. This is particularly useful if the original `lat` and `lon` inputs are column vectors.

## Background

Finding the mean position of geographic points is more complicated than simply averaging the latitudes and longitudes. `meanm` determines mean position through three-dimensional vector addition. See Geographic Statistics for Point Locations on a Sphere in the Mapping Toolbox User's Guide.

## Examples

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Create some random latitudes.

```rng(0,'twister') lats = rand(3)```
```lats = 3×3 0.8147 0.9134 0.2785 0.9058 0.6324 0.5469 0.1270 0.0975 0.9575 ```

Create some random longitudes.

`lons = rand(3)`
```lons = 3×3 0.9649 0.9572 0.1419 0.1576 0.4854 0.4218 0.9706 0.8003 0.9157 ```

Calculate the mean positions of the input geographic positions.

```[latmean,lonmean] = meanm(lats,lons,'radians'); [latmean,lonmean]```
```ans = 1×6 0.6519 0.5581 0.6146 0.7587 0.7351 0.4250 ```