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A `multi-value`

metrics aggregation that computes stats over numeric values extracted from the aggregated documents. These values can be extracted either from specific numeric fields in the documents, or be generated by a provided script.

The `extended_stats`

aggregations is an extended version of the `stats`

aggregation, where additional metrics are added such as `sum_of_squares`

, `variance`

, `std_deviation`

and `std_deviation_bounds`

.

Assuming the data consists of documents representing exams grades (between 0 and 100) of students

{ "aggs" : { "grades_stats" : { "extended_stats" : { "field" : "grade" } } } }

The above aggregation computes the grades statistics over all documents. The aggregation type is `extended_stats`

and the `field`

setting defines the numeric field of the documents the stats will be computed on. The above will return the following:

{ ... "aggregations": { "grade_stats": { "count": 9, "min": 72, "max": 99, "avg": 86, "sum": 774, "sum_of_squares": 67028, "variance": 51.55555555555556, "std_deviation": 7.180219742846005, "std_deviation_bounds": { "upper": 100.36043948569201, "lower": 71.63956051430799 } } } }

The name of the aggregation (`grades_stats`

above) also serves as the key by which the aggregation result can be retrieved from the returned response.

By default, the `extended_stats`

metric will return an object called `std_deviation_bounds`

, which provides an interval of plus/minus two standard
deviations from the mean. This can be a useful way to visualize variance of your data. If you want a different boundary, for example
three standard deviations, you can set `sigma`

in the request:

`sigma`

can be any non-negative double, meaning you can request non-integer values such as `1.5`

. A value of `0`

is valid, but will simply
return the average for both `upper`

and `lower`

bounds.

### Standard Deviation and Bounds require normality

The standard deviation and its bounds are displayed by default, but they are not always applicable to all data-sets. Your data must be normally distributed for the metrics to make sense. The statistics behind standard deviations assumes normally distributed data, so if your data is skewed heavily left or right, the value returned will be misleading.

Computing the grades stats based on a script:

{ ..., "aggs" : { "grades_stats" : { "extended_stats" : { "script" : "doc['grade'].value" } } } }

The `script`

parameter expects an inline script. Use `script_id`

for indexed scripts and `script_file`

for scripts in the `config/scripts/`

directory.

It turned out that the exam was way above the level of the students and a grade correction needs to be applied. We can use value script to get the new stats:

{ "aggs" : { ... "aggs" : { "grades_stats" : { "extended_stats" : { "field" : "grade", "script" : "_value * correction", "params" : { "correction" : 1.2 } } } } } }