Marks of six students are tabulated below:

From the population, tabulated above, you are supposed to choose a sample of size two.

(a) Determine, how many samples of size two are possible

(b) Construct sampling distribution of means by taking samples of size 2 and organize the data.

(a) To determine how many samples of size two are possible from the population of six students, we need to calculate the number of combinations of two students that can be chosen from the six. The formula for combinations is given by:

C(n,r)=n!r!(n−r)!C(n, r) = \frac{n!}{r!(n-r)!}

where nn is the total number of elements (in this case, 6 students), and rr is the number of elements to be chosen (in this case, 2 students). Applying this formula:

C(6,2)=6!2!(6−2)!=6×52×1=15C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15

So, there are 15 possible samples of size two.

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