how to scale numeric data?

Question

There are students applying for a program of study in a college. They all have passed the same prerequisite courses in a certificate level in the college, and now their unweighted GPA (0-4) is submitted for selection process together with some other scores from other categories.

The director of the program specifies for GPA 40 points from total 93 points she has given to all different categories. The lowest GPA allowed to participate in this competition is 2.5.

There is another category which is a standardized test, and students have been given scores in the form of percentage. The lowest percentage allowed to compete is 70 percent. The director of the program has assigned 30 points for this standardized test. The table she prepared for assigning the relevant point to the achieved score of each student has two columns one for percentage score which she has started from 64, assigning zero to it; and the successive rows contain 65, 66, 67, ...100. the other column which is the points column starts with 0 as I said opposite to 64, and then 0.83 opposite to 65, 1.66(0.83*2) opposite to 66, ..., 30 opposite to 100.

Would you please let me know how the table according to which each student's point for his or her GPA should be assigned will look like? ( The lowest GPA allowed to participate in this competition is 2.5.)The selection process is solely based on who has got the highest score after summing up the points from all the categories with total possible points of 93.

Thank you very much

Answer 1

Wow, a verbal mine field. Let me summarize.

1. A maximum of 93 points are assigned for evaluation for student participation in a program.
2. These 93 points are distributed among multiple sources, two of which are mentioned.
3. One source is grade point average (GPA) with contributes a maximum of 40 points, these are what can be called GPApoints.
4. Another source is a standardized test which will contribute a maximum of 30 points, or STpoints.
5. An additional 23 points will be assigned by other non specified sources.
6. The sum of the GPApoints, STpoints, and other points will range from 0 to 93 points.

The 40 points assigned for the GPA will be assigned (assuming linear relationship) for GPA values between 2.5 and 4.0. The scope of GPA is 1.5, the lowest point value is 0 the highest 40, Thus the point value assigned will follow the following equation GPApoints = (GPA-2.5)* (40/1.5). It can be seen that a GPA of 2.5 generates GPApoints value of 0, a GPA of 4.0 generates GPApoints value of 40, and a GPA of 3.25 generates a GPApoints value of 20. This is your distribution.

If an integer distribution of points is desired (for a table) there are 41 possible values from 0 to 40. Evenly divide the formula outcomes among these 41 brackets to get the assigned GPApoints value.

It was not specified in the question that the point scores for GPApoints be integer values. Since GPA scores are often given to the hundredths place the above formula gives decimal output. Also,since the example given for the standardized test which should have assigned points for scores between 70 and 100 actually assigned points for scores between 64 and 100 it is not clear how the instructor really wants to break down the assignment. I would use the following formula to assign 41 different outcomes between 0 and 40 to the GPApoints outcomes. But this is a guess as the assignment of values to the standardized score do not follow the initial instructions.

GPAscore = Round (GPApoints + 0.5)

where the function Round() is numeric rounding down to a single digit (no decimal)