The following data represents the number of goals scored by a football team in 10 matches.
2, 3, 1, 4, 2, 5, 2, 3, 2, 4

The mode of the above data is x. If one more match is played, and the team scores 3 goals, what will be the difference between the previous mode and the new mode?

The correct option is 0.

To find the mode of the data, we first need to determine the frequency of each number of goals scored in the first 10 matches.
The given data is: 2, 3, 1, 4, 2, 5, 2, 3, 2, 4

Let's count the occurrences (frequency) of each score:

Score 1: 1 time
Score 2: 4 times
Score 3: 2 times
Score 4: 2 times
Score 5: 1 time

The mode is the value that appears most frequently in a data set. Since the score of 2 occurs the most number of times (4 times), the previous mode is:
$x=2$

Now, if one more match is played and the team scores 3 goals, we add one more '3' to our data set.
The new data set becomes: 2, 3, 1, 4, 2, 5, 2, 3, 2, 4, 3

Let's recount the frequencies for the new data set:

Score 1: 1 time
Score 2: 4 times
Score 3: 3 times
Score 4: 2 times
Score 5: 1 time

In this new data set, the score of 2 still has the highest frequency (4 times). Therefore, the new mode is also 2.

Finally, we calculate the difference between the previous mode and the new mode:
$\text{Difference}=\text{Previous Mode}-\text{New Mode}$
$\text{Difference}=2-2=0$

Thus, the difference between the previous mode and the new mode is 0.