How are marks bell-curved?

The bell curve comes from plotting phenomena with a normal distribution (inverted bell actually). An example is rolling 2 dice. There is only one way to roll 2 or 12. There are 2 ways of rolling 3 and 11, 3 ways of rolling 4 and 10, 4 ways to roll 5 or 9, 5 ways to roll 6 or 8, and 6 ways to roll 7. Plotting this would look more like a mountain than an inverted bell curve but as you add more dice it would look more inverted bell-like. For grading it produces a middle heavy distribution. For example, the top 5% of students might receive an ‘A’, the next 15% a ‘B’, the middle 60% a ‘C’, the next lower 15% a ‘D’ and the unlucky bottom 5% ‘F.’ This makes grades competitive. In a class of 20 only the one top student would receive an ‘A.’ No mater how good the class as a whole did the bottom student would still fail. Some law schools use this system and there a C+ average is something to be proud of since the same work at other schools would result in a much higher grade point average. When instructors “grade on a curve” they usually mean simply adding points to harder tests to bring the average score to a C rather than applying the bell curve distribution. Instructors often design tests to produce a nice bell curve by making half the questions easy, a third or so difficult, and the last sixth almost impossible.

When a lot of data is collected about something to do with human characteristics or performance levels (e.g. height at age 19, weight at age 19 and percentage marks on an educational assessment), it is found that most people tend towards the average. . Thus given a large number of 19 year old women a large number of them will be very near to the average height of roughly 64 inches, a moderate number will be a bit above at 66 inches and a bit below at 62 inches and only a rather small number at around 60 inches or 68 inches. If you construct a vertical bar chart showing height in inches on the horizontal axis, and percentage of 19 year old women found to have each specific height, you would observe that the bars on the chart reach heights that follow a commonly found characteristic bell-shaped curve that is identified as the “normal distribution”. . Similar curves would occur for weight in pounds - with the peak on the bell-shaped normal distribution curve occuring at about 125 pounds - with a significant number of people weighing around 115 pound and 135 pounds, but few around 100 pounds or 180 pounds. Plotting such weights onto a vertical bar chart will also give bar peaks which follow a bell shaped curve, though weight curves tend to be rather more “skewed than those for height. . Examinations for assessment / grading purposes are not designed to be so hard that everyone fails with zero marks, nor so easy that everyone passes with full marks.
. They are designed so that the average student who has applied him or herself properly to the course will attain a comfortable pass mark well above the fail grades and well below the “Distinction” grades that identify the truely exceptional students. . Plotting the number of students obtaining each possible grade or percentage mark should (on a well designed assignment / examination ) result in a characteristic bell shaped curve with most people attaining a comfortable pass grade, a fair number being slightly above or below a comfortable pass grade ( “Credit” grade and “Referral” grade) and very few being exceptional “Distinction” Grade or outright abysmal Failures. . The following link provides a deeper insight into the so called “Normal Distribution - which is the most frequently encountered bell-shaped curve. . http://funadvice.com/r/bnepbg4ud87 .

– Best wishes - Majikthise. .