This paper examines what can be learned from a single trajectory when the statistical behavior of a chaotic system changes over time. It uses the Lorenz equations with a time-varying parameter as a simplified setting for questions that arise in a changing climate. Temporal averages along one realization are compared with ensemble averages across many realizations. The comparisons show that time averages can remain informative when the parameter produces sufficiently slow and smooth changes in the dynamics. Readers get a concrete way to think about nonstationary statistics and the conditions under which a moving average can meaningfully represent an evolving distribution.