- To construct the pie chart for exercise books, calculate the total (\(90\)) and find individual sector angles: Nene (\(64^\circ\)), Maundu (\(56^\circ\)), Ann (\(60^\circ\)), Mustafa (\(72^\circ\)), and Asha (\(108^\circ\)).
- To find the angle for boys at the meeting, find the total population (\(840\)) and use the proportion of boys (\(\frac{168}{840}\)) multiplied by \(360^\circ\).
- The angle for boys is \(\boxed{72^\circ}\).
Explanation
- Representing exercise books in a pie chart
To create a pie chart for the exercise books, we first need to determine the total number of books distributed. Summing the values given for each pupil:
\[T_1 = 16 + 14 + 15 + 18 + 27 = 90\]
Next, to find the size of each slice in the pie chart, we calculate the central angle for each pupil using the formula \(\text{Angle} = \left( \frac{\text{Count}}{\text{Total}} \right) \cdot 360^\circ\).
- Nene: \(\frac{16}{90} \cdot 360^\circ = 64^\circ\)
- Maundu: \(\frac{14}{90} \cdot 360^\circ = 56^\circ\)
- Ann: \(\frac{15}{90} \cdot 360^\circ = 60^\circ\)
- Mustafa: \(\frac{18}{90} \cdot 360^\circ = 72^\circ\)
- Asha: \(\frac{27}{90} \cdot 360^\circ = 108^\circ\)
To draw the chart, you would draw a circle, use a protractor to mark these angles consecutively starting from a reference radius, and label each sector accordingly. Note that the sum of these angles is \(64^\circ + 56^\circ + 60^\circ + 72^\circ + 108^\circ = 360^\circ\), confirming our calculations are correct.
- Calculating the angle for boys in the meeting pie chart
To find the angle representing boys in the pie chart, we first calculate the total number of people attending the meeting:
\[T_2 = 210 (\text{girls}) + 168 (\text{boys}) + 336 (\text{men}) + 126 (\text{women}) = 840\]
The number of boys is \(168\). The central angle for the boys is determined by the proportion of boys relative to the total number of people, multiplied by the total degrees in a circle:
\[\text{Angle}_{\text{boys}} = \left( \frac{168}{840} \right) \cdot 360^\circ\]
Simplifying the fraction: \(\frac{168}{840} = 0.2\).
Therefore, \(\text{Angle}_{\text{boys}} = 0.2 \cdot 360^\circ = 72^\circ\).
The sector representing the boys in the pie chart will have a central angle of \(72^\circ\).
Examples
Pie charts are incredibly useful in everyday life for visualising how a whole set of data is divided into parts. For example, if you manage a household budget, you can use a pie chart to see what percentage of your income goes toward rent, food, or savings at a glance. By calculating the central angle for each category, you ensure that your visual representation is accurate and proportional, making it much easier to communicate data trends clearly to others.