Databases and SQL

Aggregation

Overview

Teaching: 10 min
Exercises: 10 min
Questions
  • How can I calculate sums, averages, and other summary values?

Objectives
  • Define aggregation and give examples of its use.

  • Write queries that compute aggregated values.

  • Trace the execution of a query that performs aggregation.

  • Explain how missing data is handled during aggregation.

We now want to calculate ranges and averages for our data. We know how to select all of the dates from the Visited table:

SELECT dated FROM Visited;
dated
1927-02-08
1927-02-10
1930-01-07
1930-01-12
1930-02-26
-null-
1932-01-14
1932-03-22

but to combine them, we must use an aggregation function such as min or max. Each of these functions takes a set of records as input, and produces a single record as output:

SELECT min(dated) FROM Visited;
min(dated)
1927-02-08

SQL Aggregation

SELECT max(dated) FROM Visited;
max(dated)
1932-03-22

min and max are just two of the aggregation functions built into SQL. Three others are avg, count, and sum:

SELECT avg(reading) FROM Survey WHERE quant='sal';
avg(reading)
7.20333333333333
SELECT count(reading) FROM Survey WHERE quant='sal';
count(reading)
9
SELECT sum(reading) FROM Survey WHERE quant='sal';
sum(reading)
64.83

We used count(reading) here, but we could just as easily have counted quant or any other field in the table, or even used count(*), since the function doesn’t care about the values themselves, just how many values there are.

SQL lets us do several aggregations at once. We can, for example, find the range of sensible salinity measurements:

SELECT min(reading), max(reading) FROM Survey WHERE quant='sal' AND reading<=1.0;
min(reading) max(reading)
0.05 0.21

We can also combine aggregated results with raw results, although the output might surprise you:

SELECT person, count(*) FROM Survey WHERE quant='sal' AND reading<=1.0;
person count(*)
lake 7

Why does Lake’s name appear rather than Roerich’s or Dyer’s? The answer is that when it has to aggregate a field, but isn’t told how to, the database manager chooses an actual value from the input set. It might use the first one processed, the last one, or something else entirely.

Another important fact is that when there are no values to aggregate — for example, where there are no rows satisfying the WHERE clause — aggregation’s result is “don’t know” rather than zero or some other arbitrary value:

SELECT person, max(reading), sum(reading) FROM Survey WHERE quant='missing';
person max(reading) sum(reading)
-null- -null- -null-

One final important feature of aggregation functions is that they are inconsistent with the rest of SQL in a very useful way. If we add two values, and one of them is null, the result is null. By extension, if we use sum to add all the values in a set, and any of those values are null, the result should also be null. It’s much more useful, though, for aggregation functions to ignore null values and only combine those that are non-null. This behavior lets us write our queries as:

SELECT min(dated) FROM Visited;
min(dated)
1927-02-08

instead of always having to filter explicitly:

SELECT min(dated) FROM Visited WHERE dated IS NOT NULL;
min(dated)
1927-02-08

Aggregating all records at once doesn’t always make sense. For example, suppose we suspect that there is a systematic bias in our data, and that some scientists’ radiation readings are higher than others. We know that this doesn’t work:

SELECT person, count(reading), round(avg(reading), 2)
FROM  Survey
WHERE quant='rad';
person count(reading) round(avg(reading), 2)
roe 8 6.56

because the database manager selects a single arbitrary scientist’s name rather than aggregating separately for each scientist. Since there are only five scientists, we could write five queries of the form:

SELECT person, count(reading), round(avg(reading), 2)
FROM  Survey
WHERE quant='rad'
AND   person='dyer';
person count(reading) round(avg(reading), 2)
dyer 2 8.81

but this would be tedious, and if we ever had a data set with fifty or five hundred scientists, the chances of us getting all of those queries right is small.

What we need to do is tell the database manager to aggregate the hours for each scientist separately using a GROUP BY clause:

SELECT   person, count(reading), round(avg(reading), 2)
FROM     Survey
WHERE    quant='rad'
GROUP BY person;
person count(reading) round(avg(reading), 2)
dyer 2 8.81
lake 2 1.82
pb 3 6.66
roe 1 11.25

GROUP BY does exactly what its name implies: groups all the records with the same value for the specified field together so that aggregation can process each batch separately. Since all the records in each batch have the same value for person, it no longer matters that the database manager is picking an arbitrary one to display alongside the aggregated reading values.

Just as we can sort by multiple criteria at once, we can also group by multiple criteria. To get the average reading by scientist and quantity measured, for example, we just add another field to the GROUP BY clause:

SELECT   person, quant, count(reading), round(avg(reading), 2)
FROM     Survey
GROUP BY person, quant;
person quant count(reading) round(avg(reading), 2)
-null- sal 1 0.06
-null- temp 1 -26.0
dyer rad 2 8.81
dyer sal 2 0.11
lake rad 2 1.82
lake sal 4 0.11
lake temp 1 -16.0
pb rad 3 6.66
pb temp 2 -20.0
roe rad 1 11.25
roe sal 2 32.05

Note that we have added quant to the list of fields displayed, since the results wouldn’t make much sense otherwise.

Let’s go one step further and remove all the entries where we don’t know who took the measurement:

SELECT   person, quant, count(reading), round(avg(reading), 2)
FROM     Survey
WHERE    person IS NOT NULL
GROUP BY person, quant
ORDER BY person, quant;
person quant count(reading) round(avg(reading), 2)
dyer rad 2 8.81
dyer sal 2 0.11
lake rad 2 1.82
lake sal 4 0.11
lake temp 1 -16.0
pb rad 3 6.66
pb temp 2 -20.0
roe rad 1 11.25
roe sal 2 32.05

Looking more closely, this query:

  1. selected records from the Survey table where the person field was not null;

  2. grouped those records into subsets so that the person and quant values in each subset were the same;

  3. ordered those subsets first by person, and then within each sub-group by quant; and

  4. counted the number of records in each subset, calculated the average reading in each, and chose a person and quant value from each (it doesn’t matter which ones, since they’re all equal).

Counting Temperature Readings

How many temperature readings did Frank Pabodie record, and what was their average value?

Solution

SELECT count(reading), avg(reading) FROM Survey WHERE quant='temp' AND person='pb';
count(reading) avg(reading)
2 -20.0

Averaging with NULL

The average of a set of values is the sum of the values divided by the number of values. Does this mean that the avg function returns 2.0 or 3.0 when given the values 1.0, null, and 5.0?

Solution

The answer is 3.0. NULL is not a value; it is the absence of a value. As such it is not included in the calculation.

You can confirm this, by executing this code:

SELECT AVG(a) FROM (
    SELECT 1 AS a
    UNION ALL SELECT NULL
    UNION ALL SELECT 5);

What Does This Query Do?

We want to calculate the difference between each individual radiation reading and the average of all the radiation readings. We write the query:

SELECT reading - avg(reading) FROM Survey WHERE quant='rad';

What does this actually produce, and why?

Ordering When Concatenating

The function group_concat(field, separator) concatenates all the values in a field using the specified separator character (or ‘,’ if the separator isn’t specified). Use this to produce a one-line list of scientists’ names, such as:

William Dyer, Frank Pabodie, Anderson Lake, Valentina Roerich, Frank Danforth

Can you find a way to order the list by surname?

Key Points