$ cat file
    A DEPT        Vp           Vs            rho         VPperVS
 ------------------------ ------------ ------------ ------------
          700     151.9218     121.9269        2.223     3.623484
        700.5      155.016     125.0216        2.223     3.541452
          701      152.842     122.8473        2.223     3.581353

$ cat test.sh 
#!/bin/bash


awk  '
  NR>2{
            ++n
            vp+=$2; vs+=$3; rho+=$4;Vp_Vs+=($2/$3)^2
            for(i=1;i<=6;i++)A[n,i]=$i
      }

END{
        vpo  = vp/n
        vs0  = vs/n
        rho0 = rho/n
        k    = Vp_Vs/n
    
        printf "Angle" OFS "p" OFS "q" OFS "r" OFS
        for(x=1;x<=n;x++)printf A[x,1] OFS;printf "\n"

for(j=-90;j<=90;j++){
                             p=cos(j)+sin(j)
                             q=-8*k*sin(j)
                             r=cos(j)-(4*k*sin(j))
                             printf j OFS p OFS q OFS r OFS 

           for(i=1;i<=n;i++){
                                   EEI=vpo*rho0*((A[i,2]/vpo)^p) * ((A[i,3]/vs0)^q) * ((A[i,4]/rho0)^r)
                                   printf EEI OFS 
                            }
                                  printf "\n"
                    }

   }' OFS="\t" CONVFMT="%5.3f" OFMT="%.2g" file

$ bash test.sh   
 Angle    p         q        r       700        700.5        701    
-90    -1.342    11.057    5.080    305.533    392.341    329.344    
-89    -0.350    10.637    5.829    304.277    394.452    328.922    
-88    0.964     0.438     1.218    336.218    346.599    339.296    
-87    1.392    -10.164    -4.512   376.060    299.780    351.326    
-86    0.540    -11.421    -6.094   384.115    291.652    353.651  
.................................................................
.................................................................
.................................................................
.................................................................
.................................................................
88    1.035    -0.438      0.780    339.237    342.608    340.241    
89    1.370    -10.637    -4.808    378.078    297.708    351.912    
90    0.446    -11.057    -5.976    382.905    292.846    353.304