2.7 Variability in estimates

We would like to estimate two features of the London Marathon runners using the sample.

• (1)

  How long does it take a runner, on average, to complete the 26 miles?

• (2)

  What is the average age of the runners?

These questions may be informative for planning the London Marathon in future years.²³²³While we focus on the mean in this chapter, questions regarding variation are often just as important in practice. For instance, we would plan an event very differently if the standard deviation of runner age was 2 versus if it was 20. We will use $x_1,\mathrm{\dots },x_{100}$ to represent the 26 mile time for each runner in our sample, and $y_1,\mathrm{\dots },y_{100}$ will represent the age of each of these participants.