Letâ€™s focus on a metric that nearly all applications should be monitoring: The number of sign-ups per day. Wouldnâ€™t it be nice to know if all of a sudden that number dropped significantly?

The first thing weâ€™ll need to do is to group users by the date they signed up,
or in other words, group users by the date they were *created.*

```
ActiveRecord::Base.connection.exec_query(
<<-SQL
SELECT COUNT(*) AS total_sign_ups, created_at::date as date
FROM users
GROUP BY created_at::date
ORDER BY created_at::date DESC
SQL
).to_a
# => [{"total_sign_ups"=>99, "date"=>"2022-07-15"}, ...]
```

Now that we know how to group users by the date they signed up, we can figure out how many users sign up per day on average.

```
ActiveRecord::Base.connection.exec_query(
<<-SQL
SELECT
AVG(users.total_sign_ups) AS sign_ups_per_day_on_average
FROM(
SELECT COUNT(*) AS total_sign_ups FROM users
GROUP BY created_at::date
)
AS users LIMIT 1
SQL
).to_a
# => [{"sign_ups_per_day_on_average"=>100}]
```

Now that we have our baseline, we can detect anomalies and be alerted when they occur.

```
sign_ups_per_day_on_average = ActiveRecord::Base.connection.exec_query(
<<-SQL
SELECT
AVG(users.total_sign_ups) AS sign_ups_per_day_on_average
FROM(
SELECT COUNT(*) AS total_sign_ups FROM users
GROUP BY created_at::date
) AS users LIMIT 1
SQL
).to_a.first["sign_ups_per_day_on_average"]
# => 100
sign_ups_today = User.where("created_at::date = ?", Time.now).count
# => 99
# This can be run in a daily cron job
if sign_ups_today < sign_ups_per_day_on_average
raise Anomaly::UserSignUpAnomaly
end
```

However, this is not the most accurate way to detect anomalies. Although there were fewer sign-ups today than the average, we were only off by one. I’d hardly consider that an anomaly. What we need to consider is standard deviation. Fortunately, PostgreSQL has us covered with its Aggregate Functions for Statistics.

We can use the **STDDEV_SAMP** function to iterate through each row and return
the standard deviation for sign-ups per day. Then, we can see if the number of
sign-ups on a particular day is within 1 standard deviation of the average.

```
result = ActiveRecord::Base.connection.exec_query(
<<-SQL
SELECT
AVG(total_sign_ups) AS sign_ups_per_day_on_average,
STDDEV_SAMP(total_sign_ups) AS standard_deviation
FROM(
SELECT COUNT(*) AS total_sign_ups FROM users
GROUP BY created_at::date
) AS users LIMIT 1
SQL
).to_a
# => [{"sign_ups_per_day_on_average"=>100, "standard_deviation"=>5}]
sign_ups_today = User.where("created_at::date = ?", Date.current).count
# => 99
lower_bounds = result.first["sign_ups_per_day_on_average"] - result.first["standard_deviation"]
# => 95
# This can be run in a daily cron job
if sign_ups_today < lower_bounds
raise Anomaly::UserSignUpAnomaly
end
```

Since the average number of sign-ups per day is 100, and the standard deviation is 5, that means in a normal distribution 68% of the time the number of sign-ups per day should be between 95 and 105 (1 standard deviation), and 95% of the time the number of sign-ups per day should be between 90 and 100 (2 standard deviations).

In our example, we’ll assume that 1 standard deviation is enough to warrant an anomaly. Since we’re only interested in a drop in sign-ups, we’ll compare the number of sign-up today with 95.

We donâ€™t have to stop there, though. We can leverage the power of SQL to tell us if the result was an anomaly without needing to use Ruby. All we need is a case statement and a sub-query.

```
result = ActiveRecord::Base.connection.exec_query(
<<-SQL
SELECT
sign_ups_today,
CASE
WHEN sign_ups_today >= sign_ups_per_day_on_average - COALESCE(standard_deviation, 0) THEN false
ELSE true
END AS anomaly
FROM(
SELECT
AVG(total_sign_ups) AS sign_ups_per_day_on_average,
STDDEV_SAMP(total_sign_ups) AS standard_deviation,
(
SELECT COUNT(*) AS sign_ups_today
FROM users
WHERE created_at::date='#{Date.current}'
)
FROM(
SELECT COUNT(*) AS total_sign_ups FROM users
GROUP BY created_at::date
) AS users
) AS sign_ups_today LIMIT 1
SQL
).to_a
# => [{"sign_ups_today"=>99, "anomaly"=>false}]
# This can be run in a daily cron job
if result.first["anomaly"]
raise Anomaly::UserSignUpAnomaly
end
```

The sub-query creates a table that returns the
**sign_ups_per_day_on_average** and the **standard_deviation**. This allows
us to use a **CASE** statement on the calculated result from those two columns
when compared to **sign_ups_today** rather than doing the calculation in Ruby.

Note that we use
COALESCE
to set the value of the **standard_deviation** to **0** if no value is returned.
This can happen when there is not enough data to calculate the standard
deviation. This fallback simply compares the number of signs up to the average
number of sign-ups.

This pattern doesnâ€™t have to be limited to user sign-ups. It can be applied to any action on your system, such as the number of items purchased per day, or the number of comments posted per day. If you find that the data you need to query doesnâ€™t exist in your system, consider tracking those events in a custom database table.