In this paper we consider a four-level W-type atom interacting with a single-mode quantized electromagnetic field in the presence of the Kerr medium. The atom and the field are initially prepared in the excited state and coherent state, respectively. The influence of the Kerr medium on the N-order squeezing and Poissonian statistics is investigated. We found that the maximum value of squeezing decreases by increasing the order N. Also, we noticed that the Kerr-like medium decreases the amount of squeezing and increases the sub-Poissonian statistics.