statistics Chapter 7

Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 14 minutes. Consider 49 of the races.

Find the median of the average running times.

Answer 1

Because marathon populations, after 30 or more of such races, follow a normal distribution of their means with an average or mean that is very close, and in theory assumed as the given population mean, then the median, because it is deemed a normal distribution of all the means of such races, should be, again in theory, equal to the mean. The median equals 147 minutes (in theory). One would have to calculate the observed means of each of the 49 races to find the actual median. Since the observed means of each of the 49 races are not given, we use the theory based on a normal distribution assumption of races held within the marathon population and assume the median equals 147 minutes.