To find the mean and the mode of the number of goals scored by the football team, we can follow these steps:

Step 1: Calculate the mean (average):
The mean is calculated as the sum of all values divided by the total number of values. In this case, it's the sum of (number of goals * number of matches) divided by the total number of matches.

Mean = \(\frac{0*3 + 1*5 + 2*7 + 3*4 + 4*1 + 5*0}{3 + 5 + 7 + 4 + 1 + 0}\)

Mean = \(\frac{0 + 5 + 14 + 12 + 4 + 0}{20}\)

Mean = \(\frac{35}{20}\)

Simplify the fraction:

Mean = \(\frac{7}{4} = 1.75\)

So, the mean is 1.75.

Step 2: Find the mode (the value that appears most frequently):

From the given data, the number of goals and the corresponding number of matches are as follows:

- 0 goals: 3 matches
- 1 goal: 5 matches
- 2 goals: 7 matches
- 3 goals: 4 matches
- 4 goals: 1 match
- 5 goals: 0 matches

The mode is the value that appears most frequently, which is 2 goals in this case.

So, the mode is 2.

Therefore, the values of the mean and the mode are 1.75 and 2, respectively.