Find unknown equation of grading curve from three points grades: 72->84, 82->90, and 85->92

[Audentes]

Hey, this is a bit theoretical. I'm wondering if its possible to find out how a curve was added to a random test, given 3 grades before and after.

72 -> 84
82 -> 90
85 -> 92

Thanks,
Aude

 

[BigBeachBanana]

Hey, this is a bit theoretical. I'm wondering if its possible to find out how a curve was added to a random test, given 3 grades before and after.

72 -> 84
82 -> 90
85 -> 92

Thanks,
Aude

No. There are various methods to curve grades, and the specific method used may not be apparent from the outcome alone.

 

[Audentes]

No. There are various methods to curve grades, and the specific method used may not be apparent from the outcome alone.

Ah, alright. Thank you!

 

[Steven G]

The are many functions f(x) such that f(72)=84, f(82) = 90 and f(85)=92.
Just plot the three points and see how many curves you can draw between them! Please try this.

 

[Audentes]

I actually got a pretty good model for the 70-100 range. Thanks!!

The are many functions f(x) such that f(72)=84, f(82) = 90 and f(85)=92.
Just plot the three points and see how many curves you can draw between them! Please try this.

 

[blamocur]

The are many functions f(x) such that f(72)=84, f(82) = 90 and f(85)=92.
Just plot the three points and see how many curves you can draw between them! Please try this.

Yeah, the plot looks pretty straightforward -- pun intended

 

[Audentes]

The are many functions f(x) such that f(72)=84, f(82) = 90 and f(85)=92.
Just plot the three points and see how many curves you can draw between them! Please try this.

 

[Audentes]

Yeah, the plot looks pretty straightforward -- pun intended

View attachment 36494

Yup. Thanks!

 

[Steven G]

First, that equation does not contain all three points.
2ndly, even if the three points did lie on a line there are still many many functions that cross those three points.
I know that three non-linear points lie on a unique circle.
A cubic equation will contain those three points.
...

 

[Dr.Peterson]

Yup. Thanks!

Your linear function is a possible way the grades might have been calculated (rounding to the nearest whole number); but extrapolating beyond the interval from 72 to 85 would be very questionable.

 

[Audentes]

First, that equation does not contain all three points.
2ndly, even if the three points did lie on a line there are still many many functions that cross those three points.
I know that three non-linear points lie on a unique circle.
A cubic equation will contain those three points.
...

Your linear function is a possible way the grades might have been calculated (rounding to the nearest whole number); but extrapolating beyond the interval from 72 to 85 would be very questionable.

Yup, I used 100 and got way above 100. I think it *could* be stretched out to like 65 to 95

 

[Dr.Peterson]

Yup, I used 100 and got way above 100. I think it *could* be stretched out to like 65 to 95

Actually, it's just a little above 100, like 100.8. Which suggests that it's entirely possible that the teach may have chosen a linear "curve" that passes through (100,100):

​

This is y = 100-(5/9)(100-x). With rounding, it gives the same results. (Are your data points real, or made up?)

 

[Audentes]

Actually, it's just a little above 100, like 100.8. Which suggests that it's entirely possible that the teach may have chosen a linear "curve" that passes through (100,100):

View attachment 36496​

This is y = 100-(5/9)(100-x). With rounding, it gives the same results. (Are your data points real, or made up?)

Very interesting. Data points are real.

i've been testing 75 too, and been getting 86, this model is 86.11. I think you may have nailed it as per the original equation.

 

[Audentes]

View attachment 36495

@Dr.Peterson
Whereas 75 on this model resulted in 85.8, not 86.11. Regardless, very close, but yours seems to be the exact one!