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And the problem is the reported 3.63 implies greater precision than is contained in the originally assigned letter grade. This value is a fiction. </p>
<p>If the school added your tuition bill incorrectly and charged you an extra thousand dollars, you would be aghast, and you would demand that they do it right. But they can calculate a GPA incorrectly, and its no biggie?</p>
<p>We also use one decimal digit in GPA calculation… and then proceed to use three decimal digits in our determination of val/sal. Our val and sal are about .008 apart right now. Shouldn’t they just be co-vals?</p>
<p>drb, a case could be made that a A gp would be 4.0000000 and B+ would b e 3.500000000 in which case a gpa reported as 3.345 would be statistically acceptable.</p>
<p>Indeed it could, but that is not what is reported, and, as I noted, the difference between 3.3 and 3.33 or 3.7 and 3.67 has consequences when GPAs are calculated to 3 significant digits. More to the point is the present calculation is mathematically incorrect which should give the math and science depts pause. (Economists make up their numbers so they don’t mind so much).</p>
<p>A real life example: D2 is a HS senior, a B student, but insisted on taking an AP science course this year. I was both pleased and nervous, happy when Physics was out due to schedule conflicts so she took Enviro instead. Enviro teacher is tough, D2 worked harder at this class than any previous, has held her own and, despite much p’ing and m’ing, has learned invaluable study skills that will serve her well in college.</p>
<p>Test, homework, lab grades are numerical, calculated to 2 digits. Second quarter, she gets a “79.5” and is given a C+. Remember, these are the senior grades sent to colleges prior to final decisions being made.</p>
<p>Could she have asked for extra credit work, argued grading, sucked up, etc. to get an 80 and therefore a B-? No doubt. Point is, she should not have to. Correctly calculated, she already earned it.</p>
<p>I completely understand the anxiety but seriously, don’t worry about it. I don’t think the colleges will be swayed too much in either direction.</p>
<p>There is no anxiety (now) - she is into schools she is happy with and that are a good match, she learned alot, she is much more ready for college, so its all good.</p>
<p>It is, however, the principal of the thing. </p>
<p>As for colleges being swayed - who knows? A kid on the bubble whose last item for admissions review is a senior transcript with a C? I could certainly see how that would tip one into the “denied” pile.</p>
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<p>No. In terms of “significant figures”, the extra digit of accuracy in the GPA is correct.
Knowing the numeric course grades to an accuracy of 0.1 apiece does in fact correspond to about 5-10 times greater accuracy
(hence an extra significant digit) in the knowledge of the GPA. This is because the grades are averaged over several dozen courses.</p>
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<p>I’m not sure what you think the question of principle is here. </p>
<p>As long as all students have their grades converted in the same way, and the method is advertised in advance
and is not rigged to favor some students over others, there’s no issue of fairness, right? </p>
<p>Also, that Lucy and Desi switch places under the two conventions is meaningless, because any change in the details of the conversion system from letter to number grades (such as using 3.3333 and 3.666666… in place of 3.3 and 3.7) would shuffle the ranking of students around a bit, with implications for scholarships etc. You might find it more aesthetically pleasing to use the conversion that turns letter grades into a linear scale, but there is no issue of fairness to decide between one conversion scheme and the other.</p>
<p>The “fairness” issue is the fact that the school calculated Lucy’s GPA incorrectly, in that it invents a 3 digit number for a value that is significant only to 2 digits, which then prevents her from maintaining a scholarship that she earned. </p>
<p>(I tried to present the converse scenario for Desi, in which by virtue of having his B+ grades scored as 3.7 instead of 3.67, and then similarly calculating the GPA to 3 digits, he gets the benefit of the incorrect calculation and keeps a scholarship he did not earn. I did not get it right although I am pretty sure it can be done.)</p>
<p>Boy, first we had ethics, then feelings, now aesthetics. It is apparently difficult for many to grasp but it is none of the above - its math.</p>
<p>Must be the two cultures.</p>
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Do you have a reference that you can point me to for this?</p>
<p>Sometimes students in statistics courses are taught to report means with one more digit of significance than the original measure. For example, if the reported values were 8.2, 9.7, 10.4, one might reasonably report that the mean was 9.47 (did I do that right?)</p>
<p>I never thought of this in the context of GPA’s though. My kids’ H.S. gives grades of A=4, B=3, C=2, no + or -, but the GPA’s are always reported to two significant digits: 3.92</p>
<p>(The H.S. does not rank. I think that this “carrying it out to the ten thousandth place” is a characteristic of schools that rank.)</p>
<p>Now my head is really spinning. How can this be taught “sometimes”?</p>
<p>Where is a math geek when you need one?</p>
<p>The problem is that if you look at an “A” or a “B” as an objective grade on a points scale, the normal 10% range is so large that it can’t be used to measure anything particularly accurately. If GPA were properly rounded, at most schools it would only have 1 digit. That would be absolutely useless.</p>
<p>I think the choice here is between using a number that isn’t mathematically rigorous and not using a number at all.</p>
<p>I’m not a math geek, but I’ll give it a try. What you’re calculating in the case of a senior who’s taken, say four years of 7 courses X 4 quarters with all Bs is:</p>
<p>336.0 (grade points)/112 (individual quarterly grades)=3.00[0]</p>
<p>The single significant digit in 336.0 is correct because no decimal places have been added.</p>
<p>And as a footnote, even if the 112 were a number below 100, it would still, as a whole number, have an unlimited number of possible significant digits. There’s no error measurement; the kid took exactly 24 courses and received exactly 112 grades. So schools could report scores to 4 significant digits.</p>
<p>I think the issue is with the presumed accuracy of the initial grade. Otherwise, every grade is a definition and has an infinite number of significant digits. If the actual grade is presumed to be completely accurate, the GPA can be rounded to any number of digits.</p>
<p>^Right. But even if you accept drb’s premise that 3.3 is an imperfect representation of something that would be accurately “measured” as 3.3333333 . . . . there’s still nothing wrong with reporting gpas to 3 significant digits.</p>
<p>I disagree with TCBH, because, as I have shown, there can be a different outcome for GPA calculation depending on whether you assign a B as 3.3 vs. 3.33.</p>
<p>But I think Marathon Man is right.</p>
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<p>This is total nonsense. “Significant digits” refers to values that are known approximately up to some accuracy. In the GPA calculation everything is known exactly, because the numerical conversions are simply <em>defined</em> to equal particular values. Which values are chosen might vary from school to school, but that has nothing to do with significant digits. </p>
<p>Now, you can view grades as being imperfectly known in a statistical sense. That is, there are some random ups and downs in the assignment of the grades. So in some statistical sense, an A-minus is 3.7 plus or minus 0.1 (or whatever level of inaccuracy you view it as). Because of the averaging over several dozen courses, the “GPA variance” will be about an order of magnitude smaller than the “individual course-grade variance”, and in that sense, the GPA is accurate to an extra digit or so beyond the accuracy of the individual course grades. Not two digits more accurate, but one digit is a safe assumption, and it’s defensible to report the second additional digit as well.</p>
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<p>The school calculated correctly as long as they followed whatever their published algorithm is for GPA computation. Which algorithm to use (one that weights A-minus by 3.7, or by 3.667, or by 3.67) is a design choice made by the school, but there is nothing to make one choice more correct than another. I guess some people would consider the uniform spacing of letter grades, keeping them exactly 1/3 apart, to be a cleaner design, but that has nothing to do with the issues you’re raising. </p>
<p>As long as Lucy and Desi have their GPAs calculated by the same algorithm, there is no problem of “fairness”. There are some algorithms that could be considered unfair, such as giving very high weight to A’s and very low weight to everything else (winner-takes-all grading), or giving essentially the same weight to all grades C and higher (pass-fail grading), but that doesn’t apply to your situation. You are complaining about some very minor difference between algorithms that produce essentially the same ranking of students, and there is nothing to say that one version is more fair or more correct than the other.</p>