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To find the median number of goals scored, we first need to count the total number of games played and arrange the data points in ascending order.
Let's count the data points shown in the dot plot:
3, 2, 4, 2, 1, 3, 2, 2, 1, 4
There are a total of 10 data points.
Now, let's rearrange the data points in ascending order:
1, 1, 2, 2, 2, 2, 3, 3, 4, 4
Since there is an even number of data points (10), we need to find the average of the two middlemost numbers to get the median.
The two middlemost numbers are the 5th and 6th numbers in the ordered list:
1, 1, 2, 2, 2, 2, 3, 3, 4, 4
The 5th and 6th numbers are both 2.
Therefore, the median number of goals scored by the boys' soccer team is 2.