Worksheets for completing tables from pie charts, showing favorite sports and favorite foods with corresponding data.

Problem Overview:

The task involves completing two tables based on the given pie charts. Each table requires filling in missing information such as frequency, fraction, percentage, and angles for the categories listed. The solution will involve analyzing the pie charts and using proportional reasoning to fill in the missing data.

---

Section A: Favorite Sport

#### Given Information:
1. Total number of responses: 216
2. Angles for each sport are provided:
- Basketball: 75°
- Netball: 80°
- Rugby: 75°
- Cricket: (Not explicitly given, but can be calculated)
- Football: (Not explicitly given, but can be calculated)

#### Steps to Solve:

1. Calculate the Angle for Cricket and Football:
- The total angle in a pie chart is 360°.
- Sum of given angles: \( 75^\circ + 80^\circ + 75^\circ = 230^\circ \).
- Remaining angle for Cricket and Football: \( 360^\circ - 230^\circ = 130^\circ \).

Since the problem does not specify how Cricket and Football are divided, we assume they are equal (as no further information is provided):
- Angle for Cricket: \( \frac{130^\circ}{2} = 65^\circ \)
- Angle for Football: \( \frac{130^\circ}{2} = 65^\circ \)

2. Calculate Frequencies:
- Frequency is proportional to the angle. The formula is:
\[
\text{Frequency} = \left( \frac{\text{Angle}}{360^\circ} \right) \times \text{Total}
\]

- Basketball:
\[
\text{Frequency} = \left( \frac{75^\circ}{360^\circ} \right) \times 216 = \frac{75}{360} \times 216 = 45
\]

- Netball:
\[
\text{Frequency} = \left( \frac{80^\circ}{360^\circ} \right) \times 216 = \frac{80}{360} \times 216 = 48
\]

- Rugby:
\[
\text{Frequency} = \left( \frac{75^\circ}{360^\circ} \right) \times 216 = \frac{75}{360} \times 216 = 45
\]

- Cricket:
\[
\text{Frequency} = \left( \frac{65^\circ}{360^\circ} \right) \times 216 = \frac{65}{360} \times 216 = 39
\]

- Football:
\[
\text{Frequency} = \left( \frac{65^\circ}{360^\circ} \right) \times 216 = \frac{65}{360} \times 216 = 39
\]

3. Calculate Fractions:
- Fraction is the ratio of the frequency to the total.
- Basketball:
\[
\text{Fraction} = \frac{45}{216} = \frac{5}{24}
\]

- Netball:
\[
\text{Fraction} = \frac{48}{216} = \frac{2}{9}
\]

- Rugby:
\[
\text{Fraction} = \frac{45}{216} = \frac{5}{24}
\]

- Cricket:
\[
\text{Fraction} = \frac{39}{216} = \frac{13}{72}
\]

- Football:
\[
\text{Fraction} = \frac{39}{216} = \frac{13}{72}
\]

#### Completed Table:

| Favorite Sport | Frequency | Fraction | Angle |
|----------------|-----------|---------------|-------|
| Basketball | 45 | \( \frac{5}{24} \) | 75° |
| Netball | 48 | \( \frac{2}{9} \) | 80° |
| Rugby | 45 | \( \frac{5}{24} \) | 75° |
| Cricket | 39 | \( \frac{13}{72} \) | 65° |
| Football | 39 | \( \frac{13}{72} \) | 65° |
| Total | 216 | | 360° |

---

Section B: Favorite Food

#### Given Information:
1. Total number of responses: Not directly given, but can be calculated.
2. Percentages for some categories are provided:
- Chinese: 20%
- Caribbean: 12.5%
- Thai: 10%
- Italian: 12.5%
- Indian: (Not explicitly given, but can be calculated)

#### Steps to Solve:

1. Calculate the Total Number of Responses:
- Frequency for Chinese is given as 20.
- Percentage for Chinese is 20%.
- Using the formula:
\[
\text{Total} = \frac{\text{Frequency}}{\text{Percentage}}
\]
\[
\text{Total} = \frac{20}{0.20} = 100
\]

2. Calculate the Frequency for Each Category:
- Chinese:
\[
\text{Frequency} = 20 \quad (\text{given})
\]

- Caribbean:
\[
\text{Frequency} = \left( \frac{12.5}{100} \right) \times 100 = 12.5 \approx 13 \quad (\text{rounding to nearest whole number})
\]

- Thai:
\[
\text{Frequency} = \left( \frac{10}{100} \right) \times 100 = 10
\]

- Italian:
\[
\text{Frequency} = \left( \frac{12.5}{100} \right) \times 100 = 12.5 \approx 13 \quad (\text{rounding to nearest whole number})
\]

- Indian:
- Sum of known frequencies: \( 20 + 13 + 10 + 13 = 56 \).
- Remaining frequency for Indian: \( 100 - 56 = 44 \).

3. Calculate Percentages for Indian:
- Indian:
\[
\text{Percentage} = \left( \frac{44}{100} \right) \times 100 = 44\%
\]

4. Calculate Angles:
- Angle is proportional to the frequency. The formula is:
\[
\text{Angle} = \left( \frac{\text{Frequency}}{\text{Total}} \right) \times 360^\circ
\]

- Chinese:
\[
\text{Angle} = \left( \frac{20}{100} \right) \times 360^\circ = 72^\circ
\]

- Caribbean:
\[
\text{Angle} = \left( \frac{13}{100} \right) \times 360^\circ = 46.8^\circ \approx 47^\circ
\]

- Thai:
\[
\text{Angle} = \left( \frac{10}{100} \right) \times 360^\circ = 36^\circ
\]

- Italian:
\[
\text{Angle} = \left( \frac{13}{100} \right) \times 360^\circ = 46.8^\circ \approx 47^\circ
\]

- Indian:
\[
\text{Angle} = \left( \frac{44}{100} \right) \times 360^\circ = 158.4^\circ \approx 158^\circ
\]

#### Completed Table:

| Favorite Food | Frequency | Percentage | Angle |
|---------------|-----------|------------|-------|
| Chinese | 20 | 20% | 72° |
| Caribbean | 13 | 12.5% | 47° |
| Thai | 10 | 10% | 36° |
| Italian | 13 | 12.5% | 47° |
| Indian | 44 | 44% | 158° |
| Total | 100 | 100% | 360° |

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Section A:} \\
\begin{array}{|c|c|c|c|}
\hline
\text{Favorite Sport} & \text{Frequency} & \text{Fraction} & \text{Angle} \\
\hline
\text{Basketball} & 45 & \frac{5}{24} & 75^\circ \\
\text{Netball} & 48 & \frac{2}{9} & 80^\circ \\
\text{Rugby} & 45 & \frac{5}{24} & 75^\circ \\
\text{Cricket} & 39 & \frac{13}{72} & 65^\circ \\
\text{Football} & 39 & \frac{13}{72} & 65^\circ \\
\hline
\text{Total} & 216 & & 360^\circ \\
\hline
\end{array} \\
\text{Section B:} \\
\begin{array}{|c|c|c|c|}
\hline
\text{Favorite Food} & \text{Frequency} & \text{Percentage} & \text{Angle} \\
\hline
\text{Chinese} & 20 & 20\% & 72^\circ \\
\text{Caribbean} & 13 & 12.5\% & 47^\circ \\
\text{Thai} & 10 & 10\% & 36^\circ \\
\text{Italian} & 13 & 12.5\% & 47^\circ \\
\text{Indian} & 44 & 44\% & 158^\circ \\
\hline
\text{Total} & 100 & 100\% & 360^\circ \\
\hline
\end{array}
\end{array}
}
\]