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)/