I have several records with a given attribute, and I want to find the standard deviation.

How do I do that?

```
module Enumerable
def sum
self.inject(0){|accum, i| accum + i }
end
def mean
self.sum/self.length.to_f
end
def sample_variance
m = self.mean
sum = self.inject(0){|accum, i| accum +(i-m)**2 }
sum/(self.length - 1).to_f
end
def standard_deviation
return Math.sqrt(self.sample_variance)
end
end
```

Testing it:

```
a = [ 20, 23, 23, 24, 25, 22, 12, 21, 29 ]
a.standard_deviation
# => 4.594682917363407
```

*01/17/2012:*

*fixing “sample_variance” thanks to Dave Sag*

It appears that Angela may have been wanting an existing library. After playing with statsample, array-statisics, and a few others, I’d recommend the descriptive_statistics gem if you’re trying to avoid reinventing the wheel.

```
gem install descriptive_statistics
```

```
$ irb
1.9.2 :001 > require 'descriptive_statistics'
=> true
1.9.2 :002 > samples = [1, 2, 2.2, 2.3, 4, 5]
=> [1, 2, 2.2, 2.3, 4, 5]
1.9.2p290 :003 > samples.sum
=> 16.5
1.9.2 :004 > samples.mean
=> 2.75
1.9.2 :005 > samples.variance
=> 1.7924999999999998
1.9.2 :006 > samples.standard_deviation
=> 1.3388427838995882
```

I can’t speak to its statistical correctness, or your comfort with monkey-patching Enumerable; but it’s easy to use and easy to contribute to.

The answer given above is elegant but has a slight error in it. Not being a stats head myself I sat up and read in detail a number of websites and found this one gave the most comprehensible explanation of how to derive a standard deviation. http://sonia.hubpages.com/hub/stddev

The error in the answer above is in the `sample_variance`

method.

Here is my corrected version, along with a simple unit test that shows it works.

in `./lib/enumerable/standard_deviation.rb`

```
#!usr/bin/ruby
module Enumerable
def sum
return self.inject(0){|accum, i| accum + i }
end
def mean
return self.sum / self.length.to_f
end
def sample_variance
m = self.mean
sum = self.inject(0){|accum, i| accum + (i - m) ** 2 }
return sum / (self.length - 1).to_f
end
def standard_deviation
return Math.sqrt(self.sample_variance)
end
end
```

in `./test`

using numbers derived from a simple spreadsheet.

```
#!usr/bin/ruby
require 'enumerable/standard_deviation'
class StandardDeviationTest < Test::Unit::TestCase
THE_NUMBERS = [1, 2, 2.2, 2.3, 4, 5]
def test_sum
expected = 16.5
result = THE_NUMBERS.sum
assert result == expected, "expected #{expected} but got #{result}"
end
def test_mean
expected = 2.75
result = THE_NUMBERS.mean
assert result == expected, "expected #{expected} but got #{result}"
end
def test_sample_variance
expected = 2.151
result = THE_NUMBERS.sample_variance
assert result == expected, "expected #{expected} but got #{result}"
end
def test_standard_deviation
expected = 1.4666287874
result = THE_NUMBERS.standard_deviation
assert result.round(10) == expected, "expected #{expected} but got #{result}"
end
end
```

I’m not a big fan of adding methods to `Enumerable`

since there could be unwanted side effects. It also gives methods really specific to an array of numbers to any class inheriting from `Enumerable`

, which doesn’t make sense in most cases.

While this is fine for tests, scripts or small apps, it’s risky for larger applications, so here’s an alternative based on @tolitius’ answer which was already perfect. This is more for reference than anything else:

```
module MyApp::Maths
def self.sum(a)
a.inject(0){ |accum, i| accum + i }
end
def self.mean(a)
sum(a) / a.length.to_f
end
def self.sample_variance(a)
m = mean(a)
sum = a.inject(0){ |accum, i| accum + (i - m) ** 2 }
sum / (a.length - 1).to_f
end
def self.standard_deviation(a)
Math.sqrt(sample_variance(a))
end
end
```

And then you use it as such:

```
2.0.0p353 > MyApp::Maths.standard_deviation([1,2,3,4,5])
=> 1.5811388300841898
2.0.0p353 :007 > a = [ 20, 23, 23, 24, 25, 22, 12, 21, 29 ]
=> [20, 23, 23, 24, 25, 22, 12, 21, 29]
2.0.0p353 :008 > MyApp::Maths.standard_deviation(a)
=> 4.594682917363407
2.0.0p353 :043 > MyApp::Maths.standard_deviation([1,2,2.2,2.3,4,5])
=> 1.466628787389638
```

The behavior is the same, but it avoids the overheads and risks of adding methods to `Enumerable`

.

The presented computation are not very efficient because they require several (at least two, but often three because you usually want to present average in addition to std-dev) passes through the array.

I know Ruby is not the place to look for efficiency, but here is my implementation that computes average and standard deviation with a single pass over the list values:

```
module Enumerable
def avg_stddev
return nil unless count > 0
return [ first, 0 ] if count == 1
sx = sx2 = 0
each do |x|
sx2 += x**2
sx += x
end
[
sx.to_f / count,
Math.sqrt( # http://wijmo.com/docs/spreadjs/STDEV.html
(sx2 - sx**2.0/count)
/
(count - 1)
)
]
end
end
```

As a simple function, given a list of numbers:

```
def standard_deviation(list)
mean = list.inject(:+) / list.length.to_f
var_sum = list.map{|n| (n-mean)**2}.inject(:+).to_f
sample_variance = var_sum / (list.length - 1)
Math.sqrt(sample_variance)
end
```

If the records at hand are of type `Integer`

or `Rational`

, you may want to compute the variance using `Rational`

instead of `Float`

to avoid errors introduced by rounding.

For example:

```
def variance(list)
mean = list.reduce(:+)/list.length.to_r
sum_of_squared_differences = list.map { |i| (i - mean)**2 }.reduce(:+)
sum_of_squared_differences/list.length
end
```

(It would be prudent to add special-case handling for empty lists and other edge cases.)

Then the square root can be defined as:

```
def std_dev(list)
Math.sqrt(variance(list))
end
```

In case people are using postgres … it provides aggregate functions for stddev_pop and stddev_samp – postgresql aggregate functions

stddev (equiv of stddev_samp) available since at least postgres 7.1, since 8.2 both samp and pop are provided.

Or how about:

```
class Stats
def initialize( a )
@avg = a.count > 0 ? a.sum / a.count.to_f : 0.0
@stdev = a.count > 0 ? ( a.reduce(0){ |sum, v| sum + (@avg - v) ** 2 } / a.count ) ** 0.5 : 0.0
end
end
```

Tags: ruby