PCAT Variance Qs: Range of Scores & Similar Mean Values?

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The discussion focuses on the confusion surrounding variance questions in the PCAT, particularly regarding the use of range as a measure of variation. Participants express concern that the terminology used in the practice questions oversimplifies the concept of variance, conflating it with range, which is less precise. There is a debate about whether a larger range necessarily indicates greater variation, especially without similar mean values. While some believe visual inspection of data can provide insights into variance, others emphasize the necessity of formal calculations for accuracy. Overall, the conversation highlights the need for clearer definitions and guidelines in statistical comparisons on standardized tests.
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I'm studying for the PCAT and have come across a few variance questions. I feel like they are just oversimplying the heck out variance. I'll post one of the latest questions ...

[PLAIN]http://img825.imageshack.us/img825/1875/32561537.jpg

The explanation they give is because Class A has a larger range of scores (19 vs. 17) it "suggests" that the variation is greater. I really don't think they want me to find the expected value and then subtract each score from that and then square it and w/e else to find the exact variance. So is just looking at a range of scores a decent rule of thumb to compare variation between different data groups? Or would I need some pre-req like they atleast need to have similar mean values?
 
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mohamma1 said:
The explanation they give is because Class A has a larger range of scores (19 vs. 17) it "suggests" that the variation is greater. I really don't think they want me to find the expected value and then subtract each score from that and then square it and w/e else to find the exact variance. So is just looking at a range of scores a decent rule of thumb to compare variation between different data groups? Or would I need some pre-req like they atleast need to have similar mean values?

I don't like the terminology used in this example. It is confusing. Variance (SD^2) is a formal, well defined calculation. Range is not used that much in statistics but it's understood to be the difference between the extreme values of a sample. To lump them into a single term "variation" is a bad idea IMO.

In the example A obviously has the greater range and B the greater SD. Why confuse people with a term like "variation". At least a definition of someone's idea of what "variation" is should be provided.
 
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Yea, I completely agree. The worse part is this is an official PCAT practice, and they say 80% of the questions were on old exams so I'd be screwed if it was on the real test. Are there any good general rules I can use to find variance by just look at a set of data or graph.
 
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mohamma1 said:
Yea, I completely agree. The worse part is this is an official PCAT practice, and they say 80% of the questions were on old exams. Are they are good general rules I can use to find variance by just look at a set of data or graph.

In comparing two samples can you sometimes judge which sample has the larger variance by inspecting the data point dispersion. Otherwise you just have to calculate it. It's also difficult to judge the effect of outliers just by inspection. If you look at data point printouts enough you get a feel for it, but there's no general rule other than calculating it IMO.
 
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