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To find the new median of the dataset, we first need to arrange the numbers in ascending order:
0, 0, 0, 1, 1, 2, 2, 2, 3, 4
Since there are 10 numbers in the dataset, the median will be the average of the two middle numbers.
The two middle numbers are the 5th and 6th numbers in the arranged list: 1 and 2.
Therefore, the new median of this dataset is:
(1 + 2) / 2 = 3 / 2 = 1.5