Population and Sampling Distribution

SAMPLING DISTRIBUTIONS
|6.1 POPULATION AND SAMPLING DISTRIBUTION |

|6.1.1 Population Distribution |

Suppose there are only five students in an advanced statistics class and the midterm scores of these five students are: 70 78 80 80 95

Let x denote the score of a student.

• Mean for Population

Based on Example 1, to calculate mean for population:

[pic]

• Standard Deviation for Population

Based on example 1, to calculate standard deviation for population:

[pic]

|6.1.2 Sampling Distribution |

▪ Sample statistic such as median, mode, mean and standard deviation

6.1.2.1 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 =[pic]

Suppose we assign the letters A, B, C, D and E to scores of the five students, so that

A = 70, B = 78, C=80, D = 80, E = 95

Then the 10 possible samples of three scores each are

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE

• Sampling Error

▪ 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 =[pic]

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