Question

construct a sampling distribution of the sample mean of the population consisting of the numbers 2 5 8 11 and 14 considering a sample size of 2

Answer 1

m(2,5)=(2+5)/2=3.5

m(2,8)=(2+8)/2=5

m(2,11)=(2+11)/2=6.5

m(2,14)=(2+14)/2=8

m(5,8)=(5+8)/2=6.5

m(5,11)=(5+11)/2=8

m(5,14)=(5+14)/2=9.5

m(8,11)=(8+11)/2=9.5

m(8,14)=(8+14)/2=11

m(11,14)=(11+14)/2=12.5

Frequency

F(3.5)=F(5)=F(11)=F(12.5)=1

F(6.5)=F(8)=F(9.5)=2

Probability

$P(x)=F(x)/\sum F(x)$

P(3.5)=P(5)=P(11)=P(12.5)=0.1

P(6.5)=P(8)=P(9.5)=0.2

$E(x)=\sum P(x)x=0.1(3.5+5+11+12.5)+0.2(6.5+8+9.5)=3.2+4.8=8$

$\sigma_x^2=\sum P(x)x^2-(\sum P(x)x)^2=0.1(12.25+25+121+156.25)+0.2(38.44+64+90.25)-64=31.45+38.538-64=5.988$