- For Part 1, the sector angles for Nene, Maundu, Ann, Mustafa, and Asha are \(64^\circ\), \(56^\circ\), \(60^\circ\), \(72^\circ\), and \(108^\circ\) respectively.
- For Part 2, the angle representing the boys is calculated by finding their proportion of the total population (\(\frac{168}{840}\)) and multiplying by \(360^\circ\).
- The calculated angle for the boys is \(\boxed{72^\circ}\).
- Part 3 is incomplete and requires further information to solve.
Explanation
- Pie chart construction for exercise books
Part 1: Constructing a Pie Chart
A pie chart represents a whole quantity divided into sectors, where the size of each sector is proportional to the category's frequency.
- Calculate the Total: First, we sum the number of books to find the total:
\[ 16 + 14 + 15 + 18 + 27 = 90 \text{ books} \]
- Calculate the Angle for Each Sector: The angle for each pupil is found using the formula: \(\theta = \frac{\text{Books}}{\text{Total}} \times 360^\circ\).
- Nene: \(\frac{16}{90} \times 360^\circ = 64^\circ\)
- Maundu: \(\frac{14}{90} \times 360^\circ = 56^\circ\)
- Ann: \(\frac{15}{90} \times 360^\circ = 60^\circ\)
- Mustafa: \(\frac{18}{90} \times 360^\circ = 72^\circ\)
- Asha: \(\frac{27}{90} \times 360^\circ = 108^\circ\)
- Drawing the Chart: You would draw a circle and use a protractor to mark these angles consecutively starting from a radius. The sum of these angles is \(64^\circ + 56^\circ + 60^\circ + 72^\circ + 108^\circ = 360^\circ\), which confirms our calculations.
- Calculating the angle for boys in the meeting
Part 2: Angle representing boys
To find the angle representing boys in a pie chart, we determine their share of the total population at the meeting.
- Calculate the Total Population:
\[ T = 210 \text{ (girls)} + 168 \text{ (boys)} + 336 \text{ (men)} + 126 \text{ (women)} = 840 \text{ people} \]
- Calculate the Boys' Proportion:
\[ \text{Fraction of boys} = \frac{168}{840} = 0.2 \]
- Convert to Degrees: Multiply the fraction by the total degrees in a circle (\(360^\circ\)):
\[ \text{Angle for boys} = 0.2 \times 360^\circ = \boxed{72^\circ} \]
- Note on incomplete data
Part 3: Incomplete Data
Regarding the third part of the exercise, the text regarding Kenyi's score is incomplete. Please provide the table or the specific question you would like solved so that I can assist you further.
Examples
Pie charts are widely used in daily life to visually compare categorical data. For example, if you are tracking your monthly budget, a pie chart can clearly show which category (like rent, food, or entertainment) consumes the largest share of your income. By calculating the angles proportionally to the total amount, you create an intuitive snapshot of your financial health, making it much easier to spot where to save money! For instance, if you spend \(\$500\) out of a total \(\$2500\) budget on groceries, the angle in your chart would be \(\frac{500}{2500} \times 360^\circ = 72^\circ\).