Compute sample standard deviation, coefficient of variation and other stats over large datasets in RethinkDB using Map-Reduce in ReQL. See https://github.com/rethinkdb/rethinkdb/issues/3769#issuecomment-77229538

gistfile1.js

> load('functions.js')
> db.stuff.drop()
false
> db.stuff.insert({value:1})
> db.stuff.insert({value:2})
> db.stuff.insert({value:2})
> db.stuff.insert({value:2})
> db.stuff.insert({value:3})
> db.stuff.mapReduce(map, reduce, {finalize:finalize, out:{inline:1}}).results[0]
{
	"_id" : 1,
	"value" : {
		"sum" : 10,
		"min" : 1,
		"max" : 3,
		"count" : 5,
		"diff" : 2,
		"avg" : 2,
		"variance" : 0.4,
		"stddev" : 0.6324555320336759
	}
}

reql.py

r.table('t').group(r.row['G']).map(r.row['value']).map(lambda x: {
  'count': 1,
  'sum': x,
  'min': x,
  'max': x,
  'diff': 0 # M2,n:  sum((val-mean)^2)

}).reduce(lambda a, b: {
  'count': r.add(a['count'], b['count']),
  'sum': r.add(a['sum'], b['sum']),
  'min': r.branch(a['min'].lt(b['min']), a['min'], b['min']),
  'max': r.branch(a['max'].gt(b['max']), a['max'], b['max']),

  # See https://gist.github.com/Pyrolistical/8139958
  # diff: a.diff + b.diff + avgdelta * avgdelta * weight
  'diff': r.add(
    a['diff'],
    b['diff'],
    r.do(
      # temp helpers
      # avgdelta: a.sum/a.count - b.sum/b.count; // a.mean - b.mean
      # weight: a.count * b.count / (a.count + b.count)
      r.sub(a['sum'].div(a['count']), b['sum'].div(b['count'])),
      r.div(a['count'].mul(b['count']), a['count'].add(b['count'])),
      lambda avgdelta, weight: r.mul(avgdelta, avgdelta, weight)
    )
  )

}).ungroup().map(lambda g: {
  'G': g['group'],
  'count': g['reduction']['count'],
  'sum': g['reduction']['sum'],
  'min': g['reduction']['min'],
  'max': g['reduction']['max'],
  # sample variance
  's2': r.branch(g['reduction']['count'].gt(1), r.div(g['reduction']['diff'], g['reduction']['count'].sub(1)), 0)

}).merge(lambda d: r.do(
  r.div(d['sum'], d['count']), # avg
  r.branch(d['s2'].eq(0), 0, r.do( d['s2'], r.js('(function(x){ return Math.sqrt(x) })') )), # sample standard deviation
  lambda avg, s: {
  'avg': avg,
  's': s,
  'CV': r.branch(avg.eq(0), 0, r.div(s, avg))
}))