You have a million 32-bit floating point numbers that are in the thousands. Thus you are exceeding the 32-bitfloat precision and, if you can, you need to increase precision of the accumulator in np.mean() or change the input dtype:
a.mean(dtype=np.float32) # default and lacks precision
3067.0243839999998
a.mean(dtype=np.float64)
3045.747251076416
a.mean(dtype=np.float128)
3045.7472510764160156
b=a.astype(np.float128) b.mean()
3045.7472510764160156
Otherwise you are left to using some alternative approach to calculate the mean.
Bruce
Interesting -- I knew that float64 accumulators were used with integer arrays, and I had just assumed that 64-bit or higher accumulators would be used with floating-point arrays too, instead of the array's dtype. This is actually quite a bit of a gotcha for floating-point imaging-type tasks -- good to know!
Zach