A parameter is defined as a statistical measure pertaining to population and is based upon all units of population. Like, for example, population mean, population standard deviation (cr.), and so on.

Statistic is the measure of some characteristic of a sample in the form of the sample units. For example, sample mean (.X), moments mᵣ, sample variance, etc. Thus, the value of statistics differs from one sample to another and this is called sample fluctuation.

However, there are no fluctuations or difference in parameter and is constant.

Sampling distribution on the other hand, is known as the probability distribution of statistical data.

In statistic, the standard deviation in the sampling is known as standard error.

Example:

For a population of jive units, the values of characteristic A are:

8, 2, 6, 4, and 10

Prove that the mean of the sample means is equal to the population mean by considering possible samples of size 2 from the above series.

Solution:

The mean of the population= µ =30/5= 6

Random without replacement samplesof size 2

 

Sl no.

 

Sample values

 

Sample mean

1.

 

2.

 

3.

 

4.

 

5.

8, 2

 

8, 6

 

8, 4

 

8, 10

 

2, 6

5

 

7

 

6

 

9

 

4

 

Total

 

31

 

Sl no.

 

Sample values

 

Sample mean

6.

 

7.

 

8.

 

9.

 

10.

2, 4

 

2, 10

 

6, 4

 

6, 10

 

4, 10

3

 

6

 

5

 

8

 

7

 

Total

 

29

Mean of sample means= (31+29)/10= 60/10= 6

Therefore, mean of sample means is equal to population mean.

 

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