# Calculating averages and percentiles

## Use case

We want to understand the distribution of values for a certain numeric property
within a dataset. We're used to average values and intuitively understand how to
calculate them. However, we also know that average values can be misleading for
[skewed](https://en.wikipedia.org/wiki/Skewness) distributions which are common
in the real world: for example, 2.5 is the average value for both `(1, 2, 3, 4)`
and `(0, 0, 0, 10)`.

So, it's usually better to use
[percentiles](https://en.wikipedia.org/wiki/Percentile). Parameterized by a
fractional number `n = 0..1`, where the n-th percentile is equal to a value that
exceeds a specified ratio of values in the distribution. The
[median](https://en.wikipedia.org/wiki/Median) is a special case: it's defined
as the 50th percentile (`n = 0.5`), and it can be casually thought of as "the
middle" value. 2.5 and 0 are the medians of `(1, 2, 3, 4)` and `(0, 0, 0, 10)`,
respectively.

## Data modeling

Let's explore the data in the `users` cube that contains various demographic
information about users, including their age:

```javascript
[
  {
    "users.name": "Abbott, Breanne",
    "users.age": 52
  },
  {
    "users.name": "Abbott, Dallas",
    "users.age": 43
  },
  {
    "users.name": "Abbott, Gia",
    "users.age": 36
  },
  {
    "users.name": "Abbott, Tom",
    "users.age": 39
  },
  {
    "users.name": "Abbott, Ward",
    "users.age": 67
  }
]
```

Calculating the average age is as simple as defining a measure with the built-in
[`avg` type](/product/data-modeling/reference/types-and-formats#avg).

Calculating the percentiles would require using database-specific functions.
However, almost every database has them under names of `PERCENTILE_CONT` and
`PERCENTILE_DISC`,
[Postgres](https://www.postgresql.org/docs/current/functions-aggregate.html) and
[Snowflake](https://docs.snowflake.com/en/sql-reference/functions-aggregation)
included. For [BigQuery](https://cloud.google.com/bigquery/docs/reference/standard-sql/functions-and-operators#approx_quantiles),
you'd need to use the `APPROX_QUANTILES` function.

<CodeTabs>

```yaml
cubes:
  - name: users
    # ...

    measures:
      - name: avg_age
        type: avg
        sql: age

      - name: median_age
        type: number
        sql: PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY age)

      - name: p95_age
        type: number
        sql: PERCENTILE_CONT(0.95) WITHIN GROUP (ORDER BY age)
```

```javascript
cube("users", {
  measures: {
    avg_age: {
      sql: `age`,
      type: `avg`
    },

    median_age: {
      sql: `PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY age)`,
      type: `number`
    },

    p95_age: {
      sql: `PERCENTILE_CONT(0.95) WITHIN GROUP (ORDER BY age)`,
      type: `number`
    }
  }
})
```

</CodeTabs>

## Result

Using the measures defined above, we can explore statistics about the age of our
users.

```json
[
  {
    "users.avg_age": "52.3100000000000000",
    "users.median_age": 53,
    "users.p95_age": 82
  }
]
```

For this particular dataset, the average age closely matches the median age, and
95% of all users are younger than 82 years.

## Source code

Please feel free to check out the
[full source code](https://github.com/cube-js/cube/tree/master/examples/recipes/percentiles)
or run it with the `docker-compose up` command. You'll see the result, including
queried data, in the console.
