Sampling Error Definition

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Definition :- Sampling error is the difference between the value of a sample statistic and the value of the corresponding population parameter. In the case of mean,

Sampling error= x? - µ

Assuming that the sample is random and no non-sampling error has been made.
 
Note: - Sampling error occurs because of the chance. The difference between the values of a sample statisticobtained from a sample and the value of the corresponding population parameter obtained from the population is called the sampling error.
 
Example: -There are only five students in an advanced statistics class and midterm scores of these five students are
70        78        80        80        95

Find the sampling error.
 
Solution: - The population mean is
µ= (70+78+80+80+95)/ 5
  = 80.60

Now random sample of three scores from this population is taken and this sample includes the scores 70, 80, and 95. The mean for this sample is
            x?= (70+80+95) /3 = 81.67

Consequently,
            Sampling error= x?- µ= 81.67 – 80.60 = 1.07

 
Other example:-Consider the following population of 10 members.
20        25        13        19        9          15        11        7          17        30

Select one random sample size of five and calculate the sampling error.
 

Solution: - The population mean is
µ= (20+25+13+19+9+15+11+7+17+30) /10
  = 16.6

Now random sample size of five from this population is taken and this sample includes the scores 20, 9, 11, 17, and 30. The mean for this sample is
            x?= (20+9+11+17+30)/ 5= 17.4

Consequently,
            Sampling error= x?- µ= 17.4 – 16.6 = 0.8

 

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