How to calculate mean absolute deviation in SQL

SQL query for mean absolute deviation, run on a downloadable 30-day sample table, with the expected result and which databases support it.

In SQL, mean absolute deviation over the sample table is calculated with the query below. On the sample data it returns 4.65.

Mean absolute deviation = Average of |value − mean|

Step by step

Load daily.csv into a table called daily (day, ad_spend, website_orders, app_orders, avg_basket).
Run the query and compare with the expected result.

Table

CREATE TABLE daily (
  day INTEGER,
  ad_spend INTEGER,
  website_orders INTEGER,
  app_orders INTEGER,
  avg_basket INTEGER
);

The query

Query

SELECT ROUND(AVG(ABS(website_orders - m)), 2) AS mad_orders
FROM daily, (SELECT AVG(website_orders) AS m FROM daily) a;

Expected result on the sample data: 4.65.

What the result means

MAD is always smaller than or equal to the standard deviation for the same data. A big gap between the two points to a few extreme values.

Notes for SQL

Tested on SQLite and DuckDB; it uses only standard SQL, so it also runs on PostgreSQL, MySQL and BigQuery.
Statistical aggregates ignore NULL rows. Decide whether a missing day should be NULL (left out) or 0 (counted as a zero day).

Where mean absolute deviation misleads

MAD sometimes means median absolute deviation (from the median). They are different numbers; say which one you mean.
It is not used in most statistical tests, so keep standard deviation for those.
Excel calls it AVEDEV; pandas removed .mad() in version 2, so compute it directly.

The plain-language explanation is on the Mean absolute deviation page.

The data

daily.csv (made up): 30 days from one store
day	website_orders
1	24
2	27
3	22
4	30
5	28
6	25
7	31
8	29
9	26
10	33
11	30
12	28
13	35
14	32
15	29
16	34
17	61
18	31
19	36
20	33
21	30
22	37
23	35
24	32
25	38
26	36
27	34
28	40
29	37
30	39

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About the data on this page

The figures come from a small made-up dataset, printed above in full so you can check every number by hand. Download it as daily.csv. The results are computed from those rows when the page is built, and the Excel formulas, SQL and Python on these pages are run against the same rows before publishing, so the code and the answers agree.

To get these numbers from your own data without writing formulas, try AnalyzeIt: ask in plain words and it shows the working behind every figure.

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