## Sample & Sampling

It is one of the most important concept in the field of statistics & research.

If you want to work on the huge data , example, suppose the shopping behaviour of guys of Delhi. Then, It will be difficult to take data of all so we take a sample of suppose 200 guys from Delhi & their interpretation will tell us about the behaviour of all guys from Delhi.

Let see the difference between population and sample below in Fig.1

If you want to work on the huge data , example, suppose the shopping behaviour of guys of Delhi. Then, It will be difficult to take data of all so we take a sample of suppose 200 guys from Delhi & their interpretation will tell us about the behaviour of all guys from Delhi.

Let see the difference between population and sample below in Fig.1

Researchers use sample to draw conclusion about a population, to do this they make use of probability distribution also known as sampling distribution.

Sampling Distribution of sample mean is the distribution that one gets if they draw an infinite number of samples from population and calculate the mean of all the sample means collected.

To know the concept of Sampling Distribution of sample mean watch the link below.

https://www.youtube.com/watch?v=q50GpTdFYyI

Let us see the numerical concept of sampling distribution or probability distribution of a sample mean in

Fig 2 Below.

**Sampling Distribution of Sample Proportion**

When we are dealing with binary categorical variable then there is no sense in calclulating population mean or standard deviation but we compute proportions. But when we work on Sampling Distribution of Sample Proportion then we do have mean and standard deviation

Suppose you want to find the portion of population that uses Twitter than it will not be possible to survey everyone on earth. To solve this you will take samples and find sample proportion (Pvector).

Further we will use these sample proportion as an estimator for p .

From above theory we have two key terms as discussed below

a. Poplulation proportion (p) = population chosen / Total Population

b. Sampling proportion (p^) (p hat) = sample chosen / Total Sample

Let us see the formula for Sampling Distribution of Sample Proportion in Figure 3 below