# Random samples of size 3 are taken from a population of the numbers 3, 4,5,6, 7,8,and 9.How many samples are possible? List them and compute the mean of each sample

Random sampling is a process whereby groups of individuals are selected from a population for the purpose of research. In this case, random samples of size 3 will be taken from a population consisting of the numbers 3, 4, 5, 6, 7, 8 and 9. A sample is considered to be random when each individual in the population has an equal chance of being selected for inclusion in the study.

## Random samples of size 3 are taken from a population of the numbers 3, 4,5,6, 7,8,and 9.How many samples are possible? List them and compute the mean of each sample

There are several methods that can be used to obtain random samples of size 3 from this population. The first method involves using simple random sampling (SRS) which requires randomly selecting three numbers without replacement from the given set. This means that every possible combination must have an equal likelihood of being chosen as part of the sample group. With SRS there are 7C3 = 35 different combinations that are possible resulting in 35 different samples (1). Tthe list below provides all possible combinations:

Sample 1: {3,4,5} Sample 2: {3,4,6} Sample 3: {3,4 ,7} Sample 4: {3 ,5 ,6} Sample 5:{3 ,5 ,7} Sample 6:{3 ,6 ,7} Sample 7:{4 ,5 ,6 }Sample 8:{4,5 ,7 }Sample 9 :{4 ,6 .7 }Sample 10 :{ 5 6 7}.

The mean value for each sample can be determined by adding up all values and dividing by total number values included in each sample group (2). Therefore for example if we take our first sample with values 3 + 4+ 5= 12; 12/3= 4 and therefore our mean value would be four . After calculating all samples’ means we have a complete list below with corresponding means :

Sample 1 Mean = 4 – {(3+4+5)/3=12/3=4)}
Sample 2 Mean = 5 – {( 3+4+6)/3=13/3=5)}
Sample 3 Mean = 6 – {( 3+4 +7)/

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