Population and sample
Representative samples, simple random and systematic sampling.
Population and sample
The population (or universe) is the entire group of individuals or items about which we want information, such as all Class 12 students in a state. A sample is a part of the population that is actually studied. The number of items in the sample is the sample size, n.
Studying every member is a census. A sample survey is cheaper and quicker, and can be more careful, but it is useful only if the sample is representative, that is, it reflects the important features of the population. A sample chosen in a way that favours some members (for example, surveying only people in a library about reading habits) is biased.
Simple random sampling
In a simple random sample every member of the population has an equal chance of being selected (and every sample of size n is equally likely). Methods:
- Lottery method: write each member's name or number on identical slips, mix well and draw n slips.
- Random number tables or computer-generated random numbers.
Sampling can be with or without replacement. Without replacement from N items, the number of possible samples of size n is ᴺCₙ; for N = 8 and n = 3, there are 56.
Systematic sampling
List the population in some order and compute the sampling interval k = N/n. Choose a random starting point between 1 and k, then take every k-th item. Example: N = 500, n = 50, so k = 10. If the random start is 7, the sample is items 7, 17, 27, 37, 47, … It is simple to carry out, but can be biased if the list has a pattern that repeats with period k.
Key points
- Population: the whole group; sample: the part studied.
- A good sample is representative and free from bias.
- Simple random sampling: equal chance for every member.
- Systematic sampling: every k-th item after a random start, k = N/n.
Common mistakes
- Thinking any convenient group is a random sample.
- Confusing the sampling interval k with the sample size n.