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## Feature #12222

closed### Introducing basic statistics methods for Enumerable (and optimized implementation for Array)

**Description**

As python has statistics library for calculating mean, variance, etc. of arrays and iterators from version 3.4,

I would like to propose to introduce such features for built-in Enumerable, and optimized implementation for Array.

Especially I want to provide Enumerable#mean and Enumerable#variance as built-in features because they should be implemented by precision compensated algorithms.

The following example shows that we couldn't calculate the standard deviation for some arrays with simple variance algorithm because we get negative variance numbers.

```
class Array
# Kahan summation
def sum
s = 0.0
c = 0.0
n = self.length
i = 0
while i < n
y = self[i] - c
t = s + y
c = (t - s) - y
s = t
i += 1
end
s
end
# precision compensated algorithm
def variance
n = self.length
return Float::NAN if n < 2
m1 = 0.0
m2 = 0.0
i = 0
while i < n
x = self[i]
delta = x - m1
m1 += delta / (i + 1)
m2 += delta*(x - m1)
i += 1
end
m2 / (n - 1)
end
end
ary = [ 1.0000000081806004, 1.0000000009124625, 1.0000000099201818, 1.0000000061821668, 1.0000000042644555 ]
# simple variance algorithm
a = ary.map {|x| x ** 2 }.sum
b = ary.sum ** 2 / ary.length
p (a - b) / (ary.length - 1) #=> -2.220446049250313e-16
# precision compensated algorithm
p ary.variance #=> 1.2248208046392579e-17
```

I think precision compensated algorithm is too complicated to let users implement it.

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