The first measurement of the production rate of Xi(-)(b) baryons in pp collisions relative to that of Lambda(0 )(b)baryons is reported, using data samples collected by the LHCb experiment, and corresponding to integrated luminosities of 1, 2 and 1.6 fb(-1) at root s = 7, 8 and 13 TeV, respectively. In the kinematic region 2 < eta < 6 and p(T) < 20 GeV/c, we measure f(Xi b-)/f(Lambda b0) B(Xi(-)(b)-> J/psi Xi(-))/B(Lambda(0)(b)-> J/psi Lambda)= (10.8 +/- 0.9 +/- 0.8) x 10(-2) [root s = 7,8 TeV], f(Xi b-)/f(Lambda b0) B(Xi(-)(b)-> J/psi Xi(-))/B(Lambda(0)(b)-> J/psi Lambda) =(13.1 +/- 1.1 +/- 1.0) x 10(-2) [root s = 13 TeV], where and f(Xi b-) and f(Lambda)(b0) the fragmentation fractions of b quarks into Xi(-)(b) and Lambda(0)(b) baryons, respectively; B represents branching fractions; and the uncertainties are due to statistical and experimental systematic sources. The values of f(Xi b-)/f(Lambda b0) are obtained by invoking SU(3) symmetry in the Xi(-)(b)-> J/psi Xi(-) and Lambda(0)(b)-> J/psi Lambda decays. Production asymmetries between Xi(-)(b) and (Xi) over bar (+)(b) baryons are also reported. The mass of the Xi(-)(b) baryon is also measured relative to that of the Lambda(0)(b) baryon, from which it is found that m(Xi(-)(b)) = 5796.70 +/- 0.39 +/- 0.15 +/- 0.17 MeV/c(2), where the last uncertainty is due to the precision on the known Lambda(0)(b) mass. This result represents the most precise determination of the Xi(-)(b) mass.