Final answer:
The mode for the weights of the seven automotive students is 57 since it is the weight that occurs most frequently in the dataset provided.
Step-by-step explanation:
The question asks to determine the mode of the weights of certificate in automotive students given six of their weights and the mean weight of seven students. Since the seven students have a mean weight of 52, we can calculate the total weight by multiplying the mean by the number of students (7 x 52 = 364). By summing the given weights of the six students (53 + 49 + 57 + 46 + 50 + 57 = 312) and subtracting this from the total weight (364), we find the weight of the seventh student is 52. However, to determine the mode, which is the most frequently occurring weight in the data set, we observe that 57 appears twice, making it the mode because no other weight appears more often. The mode is therefore 57.