We report the results of $\it{in-situ}$ characterization of $^{87}$Rb atom cloud in a quadrupole Ioffe configuration (QUIC) magnetic trap after a radio-frequency (RF) evaporative cooling of the trapped atom cloud. The $\it{in-situ}$ absorption images of the atom cloud have shown clear bimodal optical density (OD) profiles which indicate the Bose–Einstein condensation (BEC) phase transition in the trapped gas. Also, we report here, for the first time, the measured variation in the sizes of the condensate and thermal clouds with the final frequency selected in the frequency scan of the RF-field for evaporative cooling. These results on frequency-dependent sizes of the clouds are consistent with the theoretical understanding of the BEC phenomenon in the trap.