. Construct a population data set for which 5, and 2.

Question

Construct a population data set for which N=6, populationman=5, and σ=2.

Answer 1

mean = sum/N = sum/6

var = sum(xi - mean)^2/N

sd = sqr(var)

10.5 8.5 6.5 3.5 1.5 -.5 have mean 5 = AM

and also have absolute average deviation of 2

var = 30.25 + 12.25 + 2.25 all doubled then divided by 6 = 2(44.75)/6 = 44.75/3

sd = sqr(44.75/3) = about 3.9

try smaller absolute deviations

8, 7, 6, 4, 3, 2 have mean 5 = midpoint = AM

and absolute deviation = 2

var = 9+4+1 double = 28, divided by 3 = 28/3

sd = sqr(28/3) = about 3

still too big

try smaller

7, 7, 6, 4, 3, 3 have mean 5

average deviation = 10/6

var = (1 + 4+ 4)2/6 = 9/3 = 3

sd = sqr3 = about 1.7 that's pretty close