At 12:20 PM 6/24/01 -0700, Melady Preece wrote:
>Hi. I am teaching educational statistics for the first time, and although I
>can go on at length about complex statistical techniques, I find myself at a
>loss with this multiple choice question in my test bank. I understand why
>the range of (b) is smaller than (a) and (c), but I can't figure out how to
>prove that it is smaller than (d).
>
>If you can explain it to me, I will be humiliated, but grateful.
>
>
>1. Which one of the following classes had
> the smallest range in IQ scores?
of course, there is nothing about the shape of the distribution of any
class ... so, does the item assume sort of normal? in fact, since each of
these classes is probably on the small side ... it would be hard to assume
that but, for the sake of the item ... pretend
in addition, it does not say to assume the population of IQ scores has mean
= 100 and sd about 15 ... so, whether this plays a role or not, i am not
sure BUT ...
> A) Class A has a mean IQ of 106
> and a standard deviation of ll.
at least about 2 units of 11 = 22 on each side of 106 ... range about 45 or
so or more
> B) Class B has an IQ range from 93
> to 119.
well, range here is about 26 ... less than in A for sure
> C) Class C has a mean IQ of 110
> with a variance of 200.
variance of 200 means an sd about 14 ... so 2 units of 14 = 28 on each side
of 110 ...
range must be 50 or more ... similar to A but, more than C
> D) Class D has a median IQ of 100
> with Q1 = 90 and Q3 = 110.
25th PR = 90 and 75PR = 110 ... IF we assumed the class was ND ... then the
mean would be about 100 too ... and since -1 for SD below the mean and +1
SD above the mean would give your roughly the 16th PR and 84th PR ... Q1
and Q3 are NOT that far out ... so, the SD must be at least 10 or more ...
thus, 2 units of at least 10 = 20 on either side of 100 = range of at least
about 40 ... probably less than A or C ... but, more than B ...
B is probably the best of the lot BUT, i am NOT sure what the real purpose
of this item is ...
>The test bank says the answer is b.
>
>Melady
>
>
>
>
>
>=================================================================
>Instructions for joining and leaving this list and remarks about
>the problem of INAPPROPRIATE MESSAGES are available at
> http://jse.stat.ncsu.edu/
>=================================================================
_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
