Question

I have to count how many points are there in each quadrant and I have only following data:
no of points having x>0, x<0, y>0 and y <0.
For ex. for following image, I’ve data
x>0 = 4 , x<0 = 3
y>0 = 4 , y<0 = 3
Is it possible to calculate no. of points in each quadrant with this much data?

Answer 1

No, there’s not enough information. For example, with your sample data, another solution would be having 4 points in the (X>0, Y>0) quadrant and 3 points in the (X<0, Y<0) quadrant.

In linear algebra terms, you have four equations with four variables:

I)   a + b = 4
II)  c + d = 3
III) a + c = 4
IV)  b + d = 3

These equations are linearly dependent (the fourth equation can be deduced from the first three: IV = I + II – III), and therefore there is not a unique solution.