Estimates are usually not exactly equal to the truth, but they get better as more data become available. We can see this by plotting a running mean from our LonMar13Samp sample. A running mean is a sequence of means, where each mean uses one more observation in its calculation than the mean directly before it in the sequence. For example, the second mean in the sequence is the average of the first two observations and the third in the sequence is the average of the first three. The running mean for the 26 mile run time in the LonMar13Samp data set is shown in Figure LABEL:netTimeRunningMean, and it approaches the true population average, 272.1001 minutes, as more data become available.
R> xBars=cumsum(LonMar13Samp[,3])/(1:100)
R> plot(xBars, type=’l’, lwd=2, ylim=c(260, 300))
Sample point estimates only approximate the population parameter, and they vary from one sample to another. If we took another simple random sample of the London Marathon runners, we would find that the sample mean for the run time would be a little different. It will be useful to quantify how variable an estimate is from one sample to another. If this variability is small (i.e. the sample mean doesn’t change much from one sample to another) then that estimate is probably very accurate. If it varies widely from one sample to another, then we should not expect our estimate to be very good.