Step 1 :The given data is [2, 3, 1, 4, 2, 3, 5, 1, 2, 3].
Step 2 :An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
Step 3 :The z-scores of the data points in the given data set were calculated and compared with a threshold value of 2 to identify any outliers.
Step 4 :No outliers were found as all the z-scores were less than the threshold.
Step 5 :Therefore, the mean was calculated with all the data points.
Step 6 :The mean hours watched per day is \(\boxed{2.6}\).
Step 7 :Final Answer: There were no apparent outliers in the data. The mean hours watched per day is \(\boxed{2.6}\).