This document discusses sampling methods and the central limit theorem. It provides details on types of probability sampling including simple random sampling, systematic sampling, stratified sampling, and cluster sampling. Simple random sampling involves randomly selecting items from a population so that each item has an equal chance of selection. Systematic sampling selects every kth item from a population. Stratified sampling divides a population into subgroups and then randomly samples from each subgroup. Cluster sampling divides a population into geographical clusters and randomly samples from each cluster. The document also explains that the central limit theorem states that the sampling distribution of sample means will approximate a normal distribution as sample size increases.

2. Group Members
1)Mohammad Wahidul Haque
111-11-1906
2)Abul kalam Azad
111-11-1770
3)Faruqul Islam
111-11-1779
4)Sohag Parvez
111-11-1772
5)Monjur Morshed Rahat
111-11-1774

3. SAMPLING METHOD &
CENTRAL LIMIT THEOREM

4. SAMPLING
 A sample is a portion or part of the population.
 Sampling is more feasible than studying the entire population.
 tool to decide something about population.
 a subset of the population.

5. Why we use Sampling ?
 To contact the whole population is time consuming.
 Sampling is less expensive than population.
 The physical impossibility of checking all the items in
the population.
 Sampling saves labor.
 The sample results are adequate.

6. There are two types of sampling :
1. Probability Sampling
2. Non-probability Sampling

7. Probability Sampling
1. Simple random sampling
2. Stratified Sampling
3. Systematic Sampling
4. Cluster Sampling

8. Simple Random Sample
 The most widely used type of sampling.
A sample selected so that each item or person in the
population has the same chance of being selected.
 is a sampling scheme with the probability that any of
the possible subsets of the sample is equally likely to
be the chosen sample.

9. Example
Suppose, a population consists of 845 employees of Nitra
Industries.
 A sample of 52 employees is to be selected from that
population.
 Every employee has same chance to be selected.
 At First, writing the name of each employee on a small slip
then depositing in a box.
 After mixing, the first selection is made drawing a slip without
looking at it until the sample of 52 employees is chosen.

10. Procedure of simple random sampling
Lottery Method:
Population is identified by some means such as by a
dice , marble etc.
 The identification are then placed in box & well
mixed.
 A sample of required size is then selected.

11. Random number method:
 A random number table is a set of integers generated.
 The table will contain all ten integers ( 0,1,2,3,…..9)
Each digit of a number has same probability of
selecting.

12. Systematic Random Sample
 It is less time consuming.
 A random starting point is selected and then every kth
member of the population is selected.
 k is calculated as the population size divided by the
sample size.
 Before using systematic random sampling, we should
carefully observe the physical order of the population.

13. Example
Suppose a population consists of 80 workers in One
composite corporation.
 A sample of 5 workers are needed to be selected.
 Here, N= 80, n=5
 K= 80/5 =16
Suppose the random starting point is 6
6,6+16,6+(16X2),6+(16X3),6+(16X4)
=6,22,38,54,70
The selection will be according to achieved numbers.

14. Stratified Random Sampling
It guarantees each group is represented in the sample.
The groups are called strata.
 A population is divided into subgroups called strata
and a sample is randomly selected from each stratum.

15. Example
 In a company there are more men and women but it is
required to have each group equally represented .Two
strata are then created . The sample of men and
women is randomly selected.

16. Cluster Sampling
It is often employed to reduce the cost of sampling a
population scattered over a large geographic area.
A population is divided into clusters using naturally
occurring geographic or other boundaries. Then,
clusters are randomly selected and a sample is
collected by randomly selecting from each cluster.

17. Example
If we need to determine the views of residents of
Dhaka about their income.
Then we have divided Dhaka into three kinds in terms
of income.
Uttara Gulshan Shymoli
Lower class Lower class Lower class
Middle class Middle class Middle class
Higher class Higher class Higher class

18. The Central Limit Theorem
 If all samples of a particular size are selected from any
population, the sampling distribution of the sample
mean is approximately a normal distribution. This
approximation improves with larger samples.

19. Why we use central limit theorem
 To determine the mean of central distribution.
 To create confident intervals.