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.
I'm not sure why you would be humiliated, even if the answer were
obvious. You can't prove the range of (b) is smaller than (d). The
question isn't even worded clearly. (b) says "a range of from 93 to
119" They range from 93 to 119 and have a range of 26 (subject to
any typographical errors I might make!), but "a range from to" is
just...sloppy. If (d) were a small class, say 2 students, the upper
and lower quartiles could be 90 and 110, depending on the precise
definition of quartile being used, and the range would be 20, even
with normality, etc.
> 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.
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