  We investigate the time averaged squared displacement (TASD) of continuous
time random walks with respect to the number of steps $N$, which the random
walker performed during the data acquisition time $T$. We prove that the TASD,
and as well the apparent diffusion constant, grow linearly with $N$, provided
the steps possess a fourth moment and can not accumulate in small intervals.
Consequently, the fluctuations of the latter are dominated by the fluctuations
of $N$, and fluctuations of the walker's thermal history are irrelevant.
Furthermore, we show that the relative scatter decays as $1/\sqrt{N}$, which
suppresses all non-linear features in a plot of the TASD against the lag time.
Parts of our arguments also hold for continuous time random walks with
correlated steps.
