online-mean

Online mean calculation (piece-by-piece)

Usage

const Mean = require('online-mean')
 
// Create a new mean object calling Mean() or new Mean()
// Each of these object stores inner variables
// So we need this extra step to be able to calculate means of multiple data flows
const m1 = Mean()
const m2 = new Mean() // same as const m2 = Mean()
 
// Update calling mean objects directly, as a function:
;[1, 2, 3, 4, 5].forEach(v => { m1(v) })
 
// Or via .fit() method. These two ways are identical!
;[4, 5, 6, 7, 8].forEach(v => { m2.fit(v) })
 
// Using  with arrays:
m1([9, 10, 11]) // Keep in mind - this line updates m1 with 3 new data values, not just averages the array
 
// Get mean value calling mean object with no arguments:
console.log('m1:', m1()) // -> 5.625
 
// Or via .value getter
console.log('m2:', m2.value) // -> 6
 
// Total number of observations:
console.log('m2 n:', m2.n) // -> 5
 
// Merge multiple mean objects:
const m3 = Mean.merge(m1, m2)
console.log('m3:', m3.value) // -> ~5.769
 
// 'n' and 'value' are not just object keys, but object getters.
// If you really need to change their values use .setN() and .setValue() methods:
m2.setValue(0)
m2.setN(0)
console.log(m2.value, m2.n) // -> 0 0

How it works

A classical formula of a sample mean is defined as follows:

ā_n = (Σ_i=1..n x_i) / n

It basically iterates over all values of x, sums them and divides on total number of samples. That works when the length of x is small and you don't need to update the mean when new values added. To calculate mean ā in on-line fashion we will use a recursive formula:

ā_n = ā_n-1 + (x_n - ā_n-1) / n

It's still based on the classical formula, however instead of summing all values we calculate ā recursively. Derivation:

ā_n = (Σ_i=1..n x_i) / n
ā_n = (Σ_i=1..n-1 x_i + x_n) / n
ā_n = ((n-1) × ā_n-1 + x_n) / n
ā_n = ā_n-1 + (-ā_n-1 + x_n) / n
ā_n = ā_n-1 + (x_n - ā_n-1) / n

To merge multiple means without iterating over all values of x, we will expand the formula a little:

ā_nm = (Σ_i=1..n x_i + Σ_j=1..m x_j) / (n + m)
ā_nm = (n * ā_n + m * ā_m) / (n + m)

Such multiplications in the numerator could produce quite big numbers, so it's better to change the expression:

ā_nm = (n * ā_n + m * ā_n - m * ā_n + m * ā_m) / (n + m)
ā_nm = ā_n + (- m * ā_n + m * ā_m) / (n + m)
ā_nm = ā_n + (ā_m - ā_n) * m / (n + m)

Much better! :)