Question

Enumerate the ordered samples that make up the unordered samples {3,3,8,8} and {1,5,5,10}.

Answer 1

For ordered sample the ordering of the observations in the sample matter while for unordered sample the ordering does not matter. For example for value 1,2 the ordered sample are {1,2} & {2,1} but unordered sample in {1,2} as for unordered sample ordering does not matter.

For unordered sample {3,3,8,8}

Number of ordered sample = 4!/(2!*2!) = 24/(2*2)=24/4= 6 [Permutation formula to find the number of ordered sample that can be created from this particular unordered sample]

So, 6 ordered sample can be created.

Answer:

Ordered sample:

1. {3,3,8,8}
2. {3,8,3,8}
3. {3,8,8,3}
4. {8,8,3,3}
5. {8,3,8,3}
6. {8,3,3,8}

For unordered sample {1,5,5,10}

Number of ordered sample = 4!/2! = 24/2=12 [Permutation formula to find the number of ordered sample that can be created from this particular unordered sample]

So, 12 ordered sample can be created in this case.

Answer:

Ordered sample:

1. {1,5,5,10}
2. {1,5,10,5}
3. {1,10,5,5}
4. {5,1,5,10}
5. {5,1,10,5}
6. {5,5,1,10}
7. {5,5,10,1}
8. {5,10,1,5}
9. ​​​​​​​{5,10,5,1}
10. {10,1,5,5}
11. {10,5,1,5}
12. {10,5,5,1}