In article <006901c0fce2$d07c7640$[EMAIL PROTECTED]>,
Melady Preece <[EMAIL PROTECTED]> 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?
> A) Class A has a mean IQ of 106
> and a standard deviation of ll.
> B) Class B has an IQ range from 93
> to 119.
> C) Class C has a mean IQ of 110
> with a variance of 200.
> D) Class D has a median IQ of 100
> with Q1 = 90 and Q3 = 110.
>The test bank says the answer is b.
>Melady
What are the sizes of the classes?
What are the distributions of the scores in the various
classes?
If the scores are random from some probability
distribution, and other than the sample data there is no
additional information about the actual scores, for other
than extremely small classes (10 is large here), not many
absolute statements can be made. I CAN tell that class C
cannot have a smaller range than 29, because otherwise the
variance cannot be 200, and scores are given as integers.
If they are not integers, it goes down slightly.
Even if the model is the totally untenable normal
distribution, the scores are RANDOM, and the samples need
not look at all normal.
As to what was bothering you, what are the quantiles
of the normal distribution?
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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