Question

a population consists of five numbers 2 3 6 8 11. consider all possible samples of size two which can be drawn without replacement from the population. find a) the mean of the population b) standard deviation of the population c) the mean of the sampling distribution of means d) the standard deviation of the sampling distribution of means

Answer 1

Acc to the question, the population consists of five numbers 2 3 6 8 11.

Therefore,

Mean(µ) = $\frac{ 2 + 3 + 6 + 8 + 11}{5}$ = 6.0

Standard deviation(σ) = $\frac{(2-6)+(3-6)+(6-6)+(8-6)+(11-6)}{5}$ = 10.8

Mean of the sampling distribution = (sum of all samples)/25 = 150/25 = 6.0 [form a matrix of elements from the set of numnbers given and finally calculate its sum]

Standard deviation of the sampling distribution = subtract the mean 6

from each number, square the result, add all 25 numbers obtained, and divide by 25. = 135/25 = 5.4

Answer 2

According  to the question, the population consists of five numbers 2 3 6 8 11.

Therefore,

Mean(µ) = $\frac{2+3+6+8+11}{5}$ = 6.0

Standard deviation(σ) = $\frac{(2-6)+(3-6)+(6-6)+(8-6)+(11-6)}{5}=10.8$

Mean of the sampling distribution = (sum of all samples)/25$= 150/25$ = 6.0 [form a matrix of elements from the set of numbers given and finally calculate its sum]

The standard deviation of the sampling distribution = subtract the mean 6

from each number, square the result, add all 25 numbers obtained, and divide by $25. = 135/25 = 5.4$

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