# Statistical aggregation

To make common statistical aggregates easier to work with in window functions and continuous aggregates, Timescale provides common statistical aggregates in a slightly different form than otherwise available in PostgreSQL and Timescale.

This example calculates the average, standard deviation, and kurtosis of a value in the `measurements` table:

`SELECT     time_bucket('10 min'::interval, ts),     average(stats_agg(val)),     stddev(stats_agg(val), 'pop'),    kurtosis(stats_agg(val), 'pop')FROM measurementsGROUP BY 1;`

This uses a two-step aggregation process. The first step is an aggregation step (`stats_agg(val)`), which creates a machine-readable form of the aggregate. The second step is an accessor. The available accessors are `average`, `stddev`, and `kurtosis`. The accessors run final calculations and output the calculated value in a human-readable way. This makes it easier to construct your queries, because it distinguishes the parameters, and makes it clear which aggregates are being re-aggregated or rolled up. Additionally, because this query syntax is used in all Timescale Toolkit queries, when you are used to it, you can use it to construct more and more complicated queries.

A more complex example uses window functions to calculate tumbling window statistical aggregates. The statistical aggregate is first calculated over each minute in the subquery and then the `rolling` aggregate is used to re-aggregate it over each 15 minute period preceding. The accessors remain the same as the previous example:

`SELECT     bucket,     average(rolling(stats_agg) OVER fifteen_min),     stddev(rolling(stats_agg) OVER fifteen_min, 'pop'),    kurtosis(rolling(stats_agg) OVER fifteen_min, 'pop')FROM (SELECT         time_bucket('1 min'::interval, ts) AS bucket,         stats_agg(val)     FROM measurements     GROUP BY 1) AS statsWINDOW fifteen_min as (ORDER BY bucket ASC RANGE '15 minutes' PRECEDING);`

For some more technical details and usage examples of the two-step aggregation method, see the blog post on aggregates or the developer documentation.

# 1D and 2D linear regression with statistical aggregates

The `stats_agg` aggregate is available in two forms, a one-dimensional aggregate shown earlier in this section, and a two-dimensional aggregate. The two-dimensional aggregate takes in two variables `(Y, X)`, which are dependent and independent variables respectively. The two-dimensional aggregate performs all the same calculations on each individual variable as performing separate one-dimensional aggregates would, and additionally performs linear regression on the two variables. Accessors for one-dimensional values append a `_y` or `_x` to the name. For example:

`SELECT     average_y(stats_agg(val2, val1)), -- equivalent to average(stats_agg(val2))    stddev_x(stats_agg(val2, val1)), -- equivalent to stddev(stats_agg(val1))    slope(stats_agg(val2, val1)) -- the slope of the least squares fit line of the values in val2 & val1FROM measurements_multival;`