elasticsearch/docs/reference/aggregations/search-aggregations-matrix-stats-aggregation.md
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---
navigation_title: "Matrix stats"
mapped_pages:
- https://www.elastic.co/guide/en/elasticsearch/reference/current/search-aggregations-matrix-stats-aggregation.html
---
# Matrix stats aggregation [search-aggregations-matrix-stats-aggregation]
The `matrix_stats` aggregation is a numeric aggregation that computes the following statistics over a set of document fields:
`count`
: Number of per field samples included in the calculation.
`mean`
: The average value for each field.
`variance`
: Per field Measurement for how spread out the samples are from the mean.
`skewness`
: Per field measurement quantifying the asymmetric distribution around the mean.
`kurtosis`
: Per field measurement quantifying the shape of the distribution.
`covariance`
: A matrix that quantitatively describes how changes in one field are associated with another.
`correlation`
: The covariance matrix scaled to a range of -1 to 1, inclusive. Describes the relationship between field distributions.
::::{important}
Unlike other metric aggregations, the `matrix_stats` aggregation does not support scripting.
::::
The following example demonstrates the use of matrix stats to describe the relationship between income and poverty.
$$$stats-aggregation-example$$$
```console
GET /_search
{
"aggs": {
"statistics": {
"matrix_stats": {
"fields": [ "poverty", "income" ]
}
}
}
}
```
The aggregation type is `matrix_stats` and the `fields` setting defines the set of fields (as an array) for computing the statistics. The above request returns the following response:
```console-result
{
...
"aggregations": {
"statistics": {
"doc_count": 50,
"fields": [ {
"name": "income",
"count": 50,
"mean": 51985.1,
"variance": 7.383377037755103E7,
"skewness": 0.5595114003506483,
"kurtosis": 2.5692365287787124,
"covariance": {
"income": 7.383377037755103E7,
"poverty": -21093.65836734694
},
"correlation": {
"income": 1.0,
"poverty": -0.8352655256272504
}
}, {
"name": "poverty",
"count": 50,
"mean": 12.732000000000001,
"variance": 8.637730612244896,
"skewness": 0.4516049811903419,
"kurtosis": 2.8615929677997767,
"covariance": {
"income": -21093.65836734694,
"poverty": 8.637730612244896
},
"correlation": {
"income": -0.8352655256272504,
"poverty": 1.0
}
} ]
}
}
}
```
The `doc_count` field indicates the number of documents involved in the computation of the statistics.
## Multi Value Fields [_multi_value_fields]
The `matrix_stats` aggregation treats each document field as an independent sample. The `mode` parameter controls what array value the aggregation will use for array or multi-valued fields. This parameter can take one of the following:
`avg`
: (default) Use the average of all values.
`min`
: Pick the lowest value.
`max`
: Pick the highest value.
`sum`
: Use the sum of all values.
`median`
: Use the median of all values.
## Missing Values [_missing_values_3]
The `missing` parameter defines how documents that are missing a value should be treated. By default they will be ignored but it is also possible to treat them as if they had a value. This is done by adding a set of fieldname : value mappings to specify default values per field.
$$$stats-aggregation-missing-example$$$
```console
GET /_search
{
"aggs": {
"matrixstats": {
"matrix_stats": {
"fields": [ "poverty", "income" ],
"missing": { "income": 50000 } <1>
}
}
}
}
```
1. Documents without a value in the `income` field will have the default value `50000`.