A population consist of five (5) measurements 2,3,5,6 and 7. What is the variance of the sampling distribution?

Question

A population consist of five (5) measurements 2,3,5,6 and 7. What is the variance of the sampling distribution?

a.

0.89

b.

1.29

c.

3.90

d.

2.20

Answer 1

2+3+5+6+7 = 23

the mean = 23/5 = 4.6

sum the squared differences from the mean

(2-4.6)^2 + (3-4.6)^2 + (5-4.6)^2 + (6-4.6)^2 + (7-4.6)^2

= 2.6^2 + 1.6^2 + .4^2 + 1.4^2 + 2.4^2

= 6.76 + 2.56 + .16 + 1.96 + 5.76

= 17.2

then divide by the degrees of freedom, either 5 if it's from the population or 4 if from a sample

to get the variance

17.2/5 = 3.44 or 17.2/4 = 4.3

if a, b, c and d are your only choices, c is the "best" or closest to correct answer

standard deviation is the square root of the variance

sqr3.44 = about 1.85

sqr4.3 = about 2.07