Each number in the table below represents the number of employees at different stores in
two nearby malls.
Number of Employees in Each Store
Valley View Mall Lone Pines Mall
Determine the interquartile range for numbers of employees at each mall. Show your work or
explain your reasoning.
Which mall would you expect to have greater variability in regard to numbers of employees?
Show your work or explain your reasoning.
i think it is x = 1.2
i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.
the proof starts from the peano postulates, which define the natural
numbers n. n is the smallest set satisfying these postulates:
p1. 1 is in n.
p2. if x is in n, then its "successor" x' is in n.
p3. there is no x such that x' = 1.
p4. if x isn't 1, then there is a y in n such that y' = x.
p5. if s is a subset of n, 1 is in s, and the implication
(x in s => x' in s) holds, then s = n.
then you have to define addition recursively:
def: let a and b be in n. if b = 1, then define a + b = a'
(using p1 and p2). if b isn't 1, then let c' = b, with c in n
(using p4), and define a + b = (a + c)'.
then you have to define 2:
def: 2 = 1'
2 is in n by p1, p2, and the definition of 2.
theorem: 1 + 1 = 2
proof: use the first part of the definition of + with a = b = 1.
then 1 + 1 = 1' = 2 q.e.d.
note: there is an alternate formulation of the peano postulates which
replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the
definition of addition to this:
def: let a and b be in n. if b = 0, then define a + b = a.
if b isn't 0, then let c' = b, with c in n, and define
a + b = (a + c)'.
you also have to define 1 = 0', and 2 = 1'. then the proof of the
theorem above is a little different:
proof: use the second part of the definition of + first:
1 + 1 = (1 + 0)'
now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 q.e.d.
hey there : ) your answer would be a.