The correct option is B Categorical: (4) only
Numerical: (1), (2)and (3)
Let us look into the datasets one by one.
1) Weights of twelve 6th graders.
Since the weight of twelve 6th graders are associated with a numerical value, the dataset is Numerical.
2) Hours of sleep that ten 7th graders slept on a school night.
Since the number of hours that ten 7th graders spend sleeping is associated with a numerical value, the dataset is Numerical.
3) Number of hours spent by Middle schoolers playing video games over a week.
Since the number of hours that spent by middle schoolers playing video games is associated with a numerical value, the dataset is Numerical.
4) Video games played by students from a certain grade.
There is no numerical value assiciated with the video games played by the students. This data can refer to the genre of the game or the name of the game or something else assiciated with the game. Hence the dataset is Categorical.
Hence, the solution is:
Categorical: (4) only
Numerical: (1), (2)and (3)