In this paper, we applied a variety of statistical methods to study gravity waves in the troposphere and lower stratosphere in the Brazilian sector, using an unprecedented large database from Instituto de Controle do Espaço Aéreo (ICEA) of radiosonde measurements carried out in 2014 on 32 locations in the Brazilian territory totaling 49,652 wind profiles. The average wind profiles were computed and classified by means of a hierarchical cluster analysis. The kinetic and potential energy densities of the gravity waves were determined using a detrending technique based on the least squares method and the Fast Fourier Transform. The time series of the energy densities were analyzed in detail and some persistent and seasonal behavior was found in some cases. A systematic search for quasi monochromatic waves was carried out and the main characteristics of such waves propagating in the troposphere and the lower stratosphere were found. The correlation analysis between the troposphere and the lower ionosphere based on parameters observed on both layers was used to investigate the wave coupling between the two layers. The results we found have implications in the so-called seeding problem of the equatorial ionospheric irregularities.