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# interpolated_average()

> Calculate the time-weighted average over an interval, while interpolating the interval bounds

export const PG = 'Postgres';

<Icon icon="tag" iconType="duotone" /> Since [1.14.0][toolkit-1.14.0]

Calculate the time-weighted average over an interval, while interpolating the interval bounds.

Similar to [`average`][average], but allows an accurate calculation across interval bounds when data has been bucketed
into separate time intervals, and there is no data point precisely at the interval bound. For example, this is useful in
a window function.

Values from the previous and next buckets are used to interpolate the values at the bounds, using the same interpolation
method used within the TimeWeightSummary itself.

Equal to [`interpolated_integral`][interpolated_integral] divided by the elapsed time.

## Samples

Calculate the time-weighted daily average of the column `val`, interpolating over bucket bounds using the 'last
observation carried forward' method:

```sql theme={"dark"}
SELECT
    id,
    time,
    interpolated_average(
        tws,
        time,
        '1 day',
        LAG(tws) OVER (PARTITION BY id ORDER by time),
        LEAD(tws) OVER (PARTITION BY id ORDER by time)
    )
FROM (
    SELECT
        id,
        time_bucket('1 day', ts) AS time,
        time_weight('LOCF', ts, val) AS tws
    FROM foo
    GROUP BY id, time
) t
```

## Arguments

The syntax is:

```sql theme={"dark"}
interpolated_average(
    tws TimeWeightSummary,
    start TIMESTAMPTZ,
    interval INTERVAL
    [, prev TimeWeightSummary]
    [, next TimeWeightSummary]
) RETURNS DOUBLE PRECISION
```

| Name     | Type              | Default | Required | Description                                                                                                                                                                                                                                                          |
| -------- | ----------------- | ------- | -------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| tws      | TimeWeightSummary | -       | ✔        | The input TimeWeightSummary from a time\_weight() call                                                                                                                                                                                                               |
| start    | TIMESTAMPTZ       | -       | ✔        | The start of the interval which the time-weighted average should cover (if there is a preceding point)                                                                                                                                                               |
| interval | INTERVAL          | -       | ✔        | The length of the interval which the time-weighted average should cover                                                                                                                                                                                              |
| prev     | TimeWeightSummary | NULL    |          | The TimeWeightSummary from the prior interval, used to interpolate the value at `start`. If NULL, the first timestamp in `tws` is used for the starting value. The prior interval can be determined from the {PG} [`lag()`][pg-window-functions] function            |
| next     | TimeWeightSummary | NULL    |          | The TimeWeightSummary from the next interval, used to interpolate the value at `start` + `interval`. If NULL, the last timestamp in `tws` is used for the starting value. The next interval can be determined from the {PG} [`lead()`][pg-window-functions] function |

## Returns

| Column  | Type             | Description                                                                                                                                                           |
| ------- | ---------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| average | DOUBLE PRECISION | The time-weighted average for the interval (`start`, `start` + `interval`), computed from the `TimeWeightSummary` plus end points interpolated from `prev` and `next` |

[average]: /api-reference/timescaledb-toolkit/time_weight/average

[interpolated_integral]: /api-reference/timescaledb-toolkit/time_weight/interpolated_integral

[pg-window-functions]: https://www.postgresql.org/docs/current/functions-window.html#FUNCTIONS-WINDOW-TABLE

[toolkit-1.14.0]: https://github.com/timescale/timescaledb-toolkit/releases/tag/1.14.0