Get variance and standard deviation of two numbers in two different rows/columns with sqlite / PHP

Question

I have a SQLite Database with the following structure:

rowid       ID                  startTimestamp   endTimestamp   subject
1           00:50:c2:63:10:1a   1000             1090           entrance
2           00:50:c2:63:10:1a   1100             1270           entrance
3           00:50:c2:63:10:1a   1300             1310           door1
4           00:50:c2:63:10:1a   1370             1400           entrance
.
.
.

I have prepared a sqlfiddle here: http://sqlfiddle.com/#!2/fe8c6/2

With this SQL-Query i can get the average differences between the endTime and the startTime between one row and the following row, sorted by subject and ID:

SELECT
    id,
    ( MAX(endtimestamp) - MIN(startTimestamp)
    - SUM(endtimestamp-startTimestamp)
    ) / (COUNT(*)-1) AS averageDifference
FROM
    table1
WHERE ID = '00:50:c2:63:10:1a'
AND subject = 'entrance'
GROUP BY id;

My problem: To calcute the average value is no problem, that does this query. But how can i get the standard deviation and the variance of this values?

Answer 1

First finding the time differences of interest by joining the table to itself and grouping by ID, then finding the averages, variances as V(x) = E(x^2) - (E(x))^2 and standard deviation as sqrt(V)gives

SELECT ID, AVG(diff) AS average,
       AVG(diff*diff) - AVG(diff)*AVG(diff) AS variance,
       SQRT(AVG(diff*diff) - AVG(diff)*AVG(diff)) AS stdev
FROM
    (SELECT t1.id, t1.endTimestamp,
            min(t2.startTimeStamp) - t1.endTimestamp AS diff
    FROM table1 t1
    INNER JOIN table1 t2
    ON t2.ID = t1.ID AND t2.subject = t1.subject
    AND t2.startTimestamp > t1.startTimestamp  -- consider only later startTimestamps
    WHERE t1.subject = 'entrance'
    GROUP BY t1.id, t1.endTimestamp) AS diffs
GROUP BY ID