Question

Suppose that in a race, male participants are given even entry numbers and females are given odd entry numbers. Would choosing every 10th runner to answer a survey give a representative sample to all racers? What about every 5th runner? Why?

Answer 1

No,

This is systematic sampling

Disadvantage of Systematic Sampling. The process of selection can interact with a hidden periodic trait within the population. If the sampling technique coincides with the periodicity of the trait, the sampling technique will no longer be random and representativeness of the sample is compromised.

1)

Since every 10 the runner will have same gender as 10 is even

It is not representative sample to all racers

2) since 5 is odd

Every alternate participants will be of opposite gender

Hence yes.