# Calculating Average and Percentiles

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 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.
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 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.

Let's explore the data in the `Users`

cube that contains various demographic
information about users, including their age:

```
[
{
"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.
Calculating the percentiles would require using database-specific functions. However,
almost every database has them under names of `PERCENTILE_CONT`

and `PERCENTILE_DISC`

,
Postgres and
BigQuery
included.

```
measures: {
avgAge: {
sql: `age`,
type: `avg`,
},
medianAge: {
sql: `PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY age)`,
type: `number`,
},
p95Age: {
sql: `PERCENTILE_CONT(0.95) WITHIN GROUP (ORDER BY age)`,
type: `number`,
},
},
```

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

```
[
{
"Users.avgAge": "52.3100000000000000",
"Users.medianAge": 53,
"Users.p95Age": 82
}
]
```

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

Please feel free to check out the
full source code
or run it with the `docker-compose up`

command. You'll see the result, including
queried data, in the console.

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