Even though is not the fastest choice, if performance is not an issue you can use:
sum(~np.isnan(data))
.
In [7]: %timeit data.size - np.count_nonzero(np.isnan(data))
10 loops, best of 3: 67.5 ms per loop
In [8]: %timeit sum(~np.isnan(data))
10 loops, best of 3: 154 ms per loop
In [9]: %timeit np.sum(~np.isnan(data))
10 loops, best of 3: 140 ms per loop