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A Bell curve (generally a Gaussian Curve but not always, though what you are inquiring about would be) is just where the data is laid out so the sum of the data
by yareally 13y ago
A Bell curve (generally a Gaussian Curve but not always, though what you are inquiring about would be) is just where the data is laid out so the sum of the data adds up to 1 and symmetrical around the average (with the average being the center point). Since the data adds up to one (so you would have to convert each data set to percentages). Useful when you don't know the exact distribution of the data at hand.
To give an easy to visualize example, a teacher that grades on the curve, does so by normalizing the data (taking the top 10% of the grades for a test and making those A's regardless of previous score, then making the top 10%-20% B's regardless of score and so on. There are different methods to calculate the percentiles (and what those percentiles are could vary by grading system), but that's just the most common one.
- btilly 13y agoYou're showing no sign of understanding why the bell curve is shaped like it is either. You're just describing what you've seen.
- yareally 13y agoInstead of criticizing, why don't you correct me then please by giving a better example. We're all here to learn, not to put each other down by 10 second, thoughtless replies. Your background (being just shy of a PhD in Math), should have lots of useful information you can share.
- christopheraden 13y agoI'm worried your explanation may be confusing to people in some places. The bell curve and Gaussian curve (and normal curve) are almost always synonymous. Bell Curve describes its shape, while the Gaussian curve describes the guy who derived that nasty-looking pdf. While some other distributions may look bell-shaped (especially ones that converge to a Normal in some asymptotic sense, like the t-distribution), people will look at you funny if you refer to anything other than the normal (or in rare cases, the t) as "The Bell Curve". The point about "the data is laid out so the sum of the data adds up to 1" doesn't make much sense since the Normal takes values on the entire real line. Could you clarify? The procedure you describe is not what most people would call "normalizing", so much as breaking the data up into quantiles/percentiles. Normalizing the data would be for the instructor will subtract the average from everyone's raw score, then divide by the standard deviation. If the raw scores themselves were distributed normally, then these new "normalized" scores are now standard normal, so letter grades are given based on how far away from 0 a student's scaled score is. This procedure is pretty flawed since scores are usually not super close to normality (many exams are not symmetric in scores, the distribution may have several modes, etc). The procedure you describe makes no assumptions about the underlying data, and does not require normality, so I like it more.
- yareally 13y agoSorry, by data, I meant the percentages add up to one (so that the integral equals 1), not the data it was derived from. Thanks for the correction. My method would be more fair, but is incorrect when applied to standard normalization. It should be percentiles. In a strict bell curve, if the top 20% get A's, then the bottom 20% would also have to fail (even if they didn't really get an F) so a pretty unfair system as you mentioned as grades are already predetermined :(
- christopheraden 13y agoYour first point is not just a property of the Gaussian, but of all distributions. It's the Second Axiom of Probability! Your method is incorrect as a method of normalization, but it seems we are in agreement that perhaps normalization itself is a silly method for this. Most instructors I've known that claimed they were "curving" were in fact using the percentile approach. Grading based on percentiles (top 10% get A's, next 20% get B's, 40% C's, 10% D, bottom 20% F, for example) allows you far more flexibility, as the percentiles don't even need to be symmetric. My grad courses usually only had three grades: A+, A, and "Please see me to discuss your future in the department".