A survey of 20 people was conducted on their favorite football team. The results were: Brazil (8 people), Germany (7 people), Italy (3 people), and France (2 people). Calculate the central angles for

• a) The population is the group of 20 persons. An individual is one person from this group.
• b) The character of this distribution is the favorite team. The nature of this distribution is qualitative (or categorical), as the data represents categories rather than numerical values.

The total frequency is given as 20. The sum of frequencies is $8+7+3+2=20$.
To find the central angle for each team, we use the formula:

• Brazil: $\left(\frac{8}{20}\right) \times 360^\circ = 0.4 \times 360^\circ = 144^\circ$
• Germany: $\left(\frac{7}{20}\right) \times 360^\circ = 0.35 \times 360^\circ = 126^\circ$
• Italy: $\left(\frac{3}{20}\right) \times 360^\circ = 0.15 \times 360^\circ = 54^\circ$
• France: $\left(\frac{2}{20}\right) \times 360^\circ = 0.1 \times 360^\circ = 36^\circ$

The completed table is:

The frequency for Germany is 7, and the total frequency is 20.

The percentage of persons who like the Germany team is $\boxed{\text{35\%}}$.

To draw a bar graph of frequencies:

• Draw a horizontal axis (x-axis) and label it "Favorite Team". Mark categories for Brazil, Germany, Italy, and France.
• Draw a vertical axis (y-axis) and label it "Frequency". Scale this axis from 0 up to at least 8 (the highest frequency).
• For each team, draw a vertical bar whose height corresponds to its frequency:
  • Brazil: Bar height of 8 units.
  • Germany: Bar height of 7 units.
  • Italy: Bar height of 3 units.
  • France: Bar height of 2 units.
• Ensure the bars are of equal width and are separated by small gaps.