Permutation and combination

Pauli exclusion principle as an example of nCr

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Action and stative verbs


Average of averages

Let the data be x1, x2, …, xm, and y1, y2, ..., yn.


The average of x is Σxi / m and the average of y is Σyi / n.

The average of x and y is (Σxi + Σyi) / (m+n).


If m = n, we get Σ(xi +yi) / (2n).

In this case, it is the same result as (Σxi / m + Σyi / n) / 2.


If m ≠n, we get (Σxi + Σyi) / (m+n).


In this case, it is different from (Σxi / m + Σyi / n) / 2.