Which of these is an example of systematic random sample?
a.) choosing 10 marbles from a jar containing 40 marbles.
b.) picking out 10 names from a group of 50 students.
c.) picking out the telephone number of every 20th person from a directory.
d.) selecting one card from a deck of 52 well-shuffled cards.
The Correct Answer and Explanation is :
The correct answer is c.) picking out the telephone number of every 20th person from a directory.
Explanation:
A systematic random sample is a type of sampling method where you select members from a larger population at a regular interval. This method is particularly useful when the population is large and a simple random sampling would be too cumbersome or time-consuming.
In the case of option c, selecting every 20th person from a directory illustrates systematic sampling because it involves an ordered list (the directory) and a fixed interval (every 20th person). This method ensures that the sample is spread evenly across the entire population, which can help reduce bias and provide a representative sample. The starting point is usually randomly selected, and then the selection continues at the set interval, making the process efficient and straightforward.
Conversely, the other options do not qualify as systematic random samples:
- a.) Choosing 10 marbles from a jar containing 40 marbles. This is a simple random sample if each marble has an equal chance of being chosen, but it does not involve a systematic approach or a fixed interval.
- b.) Picking out 10 names from a group of 50 students. Similar to option a, this represents a simple random sampling method if done randomly, but it lacks the systematic structure.
- d.) Selecting one card from a deck of 52 well-shuffled cards. This option describes a simple random sample where each card has an equal chance of being selected, rather than following a systematic procedure.
In summary, option c demonstrates systematic random sampling because it involves a fixed interval in the selection process, making it distinct from the other options provided. This method is beneficial in achieving a sample that is both random and evenly distributed across the population.