SAMPLING DISTRIBUTIONS6.1 POPULATION AND SAMPLING DISTRIBUTION6.1.1 Population DistributionSuppose there are only five students in an advanced statistics class and the midterm scores of these five students are:7078808095Let x denote the score of a student.Mean for PopulationBased on Example 1, to calculate mean for population:Standard Deviation for PopulationBased on example 1, to calculate standard deviation for population:6.1.2 Sampling DistributionSample statistic such as median, mode, mean and standard deviation6.1.2.1 The Sampling Distribution of the Sample Mean Reconsider the population of midterm scores of five students given in example 1. Let say we draw all possible samples of three numbers each and compute the mean.Total number of samples = 5C3 =Suppose we assign the letters A, B, C, D and E to scores of the five students, so thatA = 70,B = 78,C=80,D = 80, E = 95Then the 10 possible samples of three scores each areABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDESampling ErrorSampling 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 =Mean ( ) for the Sampling Distribution ofBased on example 2,Standard Deviation ( ) for the Sampling Distribution of