Fast way to subtract the mean from a dataset

Do this:

Standardize[data, Mean, 1 &]

Here are the timings for comparison, with f1 and f2 as defined in Mr.Wizard's answer:

big = RandomReal[{0, 50}, {1*^7, 2}];

f1[big] // RepeatedTiming // First
f2[big] // RepeatedTiming // First
Standardize[big, Mean, 1 &] // RepeatedTiming // First

0.274

0.232

0.12

This is a modest improvement on your code:

f2[data_] := (data\[Transpose] - Mean[data])\[Transpose]

With your code as a function f1 for reference:

f1[data_] := Transpose[# - Mean /@ # &[Transpose[data]]]

And now with Simon Woods's f3 calling the internal function used by Standardize in v11:

f3[data_] := 
  Module[{a = data}, Statistics`Library`MatrixRowTranslate[a, -Mean[a]]; a]

Timings:

big = RandomReal[{0, 50}, {1*^7, 2}];

f1[big] // RepeatedTiming // First
f2[big] // RepeatedTiming // First
f3[big] // RepeatedTiming // First

0.193

0.15

0.0936

f1[big] === f2[big] === f3[big]

True

---

In Mathematica 10.1 under Windows x64 Standardize performs rather poorly. I get:

Standardize[big, Mean, 1 &] // RepeatedTiming // First

0.852

I am curious to know if this is version or platform dependent, or perhaps both.