Determine weather the given values are from a discrete or continuos data set. a statistics student obtains a sample data from one of his classes and finds that the average student weighs 157.0 lbs

A continuous data set is where you can plot every point (even very, very small decimal numbers) because the unit can be measured in parts of the whole.

A discrete data set is where you can only plot the units in whole values. For example, if you were plotting the number of people, you can't have a part of a person.

Weight is measured in lbs which can be measured in parts of the lb (such as 100.005 lbs) so it is continuous.

Continuous data set

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!