B-Plot : Explanation of exponent

Lab computations :

Use the result for the electric field of a dipole as an analogy:

In the experiment we aligned a compass in the bet field due to both the Earth and a strong small magnetic rod . 

BnetcosŲ = BE
BnetsinŲ = Bmi, where i = 1, 2, 3 for the three distances between the small magnet and compass. The deflection angle made with the earth's magnetic field  grows as the distance decreases. 

Using  the hypothesis  that Bmi = constant/din , 
you measured Bm1/Bm2  = tanŲ1/ tanŲ2 = (d2/d1)n . 

You could solve for n. You repeated the computation for the two other combinations then took the average. 

Your value of n was close to 3 when your calculation was based on the two largest distances  (the pair BM1 and BM2) between the compass and the bar magnet. When your calculations for n were based on averages from the pair BM2 and BM3 and the pair BM1 and BM3, the distances between the compass and the bar magnet were smaller on the average. That's why your results for n were increasingly less than 3.