We present analyses and measurements of the readout scheme in a dispersive circuit QED system by varying detuning between the qubit frequency and the cavity resonant frequency. With larger detuning, the ground state frequency and the bright state frequency get closer and the transition power between themincreases in the cavity transmission. This implies that the relatively strong microwave power is allowed for far-detuned qubit readout. Additional number splitting peaks are also observed in qubit spectroscopy. We will discuss the relation between the difference of the ground state and the bright state frequencies and the difference of the qubit and the cavity frequencies.