GPA

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HiDoes the following sentences mean 'Hames has a higher GPA than Nector?James's grade point average puts him in the top third of the graduating class of college A. Nestor is in the top tenth of the same class. Thanks

MrGuedes · Accepted Answer

martinleeDo the following sentences mean 'James has a higher GPA than Nestor?

No. Not necessarily. The sentences are saying that James's GPA is amongst the highest ~33% of the class, whilst Nestor's GPA is amongst the highest 10% of the class.
On other words, imagine you would list the GPAs of the entire class in order, from highest to lowest. Now suppose you would separate them in three equal parts. Of those parts, James is in the part with the highest values. Suppose again the same thing, but now you would separate them in ten equal parts. Nestor is in the one of those with the highest values.

Welcome to the mathematical concept of percentiles! (Yes, your question is really mainly related to mathematics.) We know that James is above the 67th percentile, and Nestor is above the 90th. However, that alone isn't enough to tell us which one has the highest GPA.
But, even so, if the person who wrote those sentences specified a greater interval for James (between the 67th and the 100th percentile) than for Nestor (between the 90th and the 100th percentile), that means they probably wanted to infer that Nestor had a greater GPA than James, but we can't be sure of that. Maybe James's GPA is in the 95th percentile, and Nestor's is in the 92nd. We really can't tell, but we can assume Nestor is probably higher than James.

On other words, and to finalise, we can't tell for sure whose GPA is higher, but the most likely is that Nestor's GPA is higher than James's.

Mister Micawber · Answer

I think that MrGuedes is over-analyzing the logic of your sentences.  We would presume from your sentences in any ordinary context that Nestor indeed has a higher GPA than James, based solely on the percentages given.  Otherwise, there would be no point in indicating those percentages.

MrGuedes · Answer

Mister MicawberWe would presume from your sentences in any ordinary context that James indeed has a higher GPA than Nestor, based solely on the percentages given. Otherwise, there would be no point in indicating those percentages.

Excuse me, I believe you meant to say that we would assume that Nestor has a higher GPA than James, not the other way round. James is in the top third, whilst Nestor is in the top tenth. James is given an interval that includes values below those for which Nestor's interval allows. That probably means that the author wanted to convey that Nestor's GPA is higher than James's, but it does not exclude the possibility that it is the other round.

On other words, if the author specified for Nestor such a small interval as a tenth, but for James he generalised more (up to a third), we can deduce that, although James's GPA is in the top third, it is probably not in the top tenth, because, if it were, the author would probably have said it was in the top tenth, as he did for Nestor.
Now, if Nestor's GPA is in the top tenth, and James's GPA is in the top third but not in the top tenth, then Nestor's GPA is certainly higher than James's. But nowhere in those sentences is it said that James's GPA is not in the top tenth. We can only deduce that is probably the case, based on the percentages given.

Mister MicawberOtherwise, there would be no point in indicating those percentages.

Indeed, if James's GPA were also in the top tenth, like Nestor's, then why would the author say one is in the top tenth and the other in the top third? What would be the point?

That's why we can assume that Nestor's GPA is probably, but not certainly, higher than James's. If it were the other way round, it wouldn't contradict any of the information given.

Martinlee · Answer

Thanks so much.
But I still don't understand.

Martinlee · Answer

(James's grade point average puts him in the top third of the graduating class of college A. Nestor is in the top tenth of the same class.)

My understanding is that James is the third in the class, whereas Nestor is the tenth in the class.

MrGuedes · Answer

martinleeThanks so much. But I still don't understand.

Let me try to put what we are told in a scheme:

--------------------|-------|---|

These are 30 dashes (-). Imagine they are the GPA ratings of the class James and Nestor are in, sorted from lowest to highest. I've included also three pipes (|) to separate the top third, the top tenth, and the maximum.
What we are told is that James's GPA is between the first and the third pipes (in the top third), and that Nestor's GPA is between the second and the third (in the top tenth).

That's all we know. Now you can deduce that it is most likely that Nestor's GPA is higher than James's, because James is given an interval that extends below the interval that Nestor is given.
In fact, we can deduce it is most likely that James's GPA is not in the top tenth (i.e., only between the first and the second pipes), because, if it were also in the top tenth (i.e., between the second and third pipes), like Nestor's GPA, the author would probably have said that James's GPA was also in the top tenth. But we can't be sure that's the case.

In conclusion, Nestor's GPA is probably higher than James's, but we can't be sure of that based solely on that information.

Mister Micawber · Answer

MrGuedes I believe you meant to say that we would assume that Nestor has a higher GPA than James, not the other way round.

That's right. I have fixed it. The rest of my post stands.

MrGuedes · Answer

martinleeMy understanding is that James is the third in the class, whereas Nestor is the tenth in the class.

No. Nothing to do with that. They are in the same class, but in different positions of the class. When it says James is in the top third and Nestor in the top tenth, that's the same as saying James is in the top ~33% and Nestor in the top 10%. Look at my scheme in my previous post.

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