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Sagot :
To represent the given data in pie charts, we need to follow a series of steps to visually convey the proportion of each category within the dataset. For each part (a through e), we will calculate the percentages or proportions and then construct a pie chart to visually represent that data.
a) Number of students from Class IV to VIII:
The table given is:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Class} & \text{IV} & \text{V} & \text{VI} & \text{VII} & \text{VIII} \\ \hline \text{No. of students} & 50 & 45 & 40 & 35 & 10 \\ \hline \end{array} \][/tex]
First, calculate the total number of students:
Total = 50 + 45 + 40 + 35 + 10 = 180
Next, compute the percentage of students in each class:
[tex]\[ \begin{array}{ll} \text{Class IV} &= \left(\frac{50}{180}\right) \times 100 = 27.78\% \\ \text{Class V} &= \left(\frac{45}{180}\right) \times 100 = 25.00\% \\ \text{Class VI} &= \left(\frac{40}{180}\right) \times 100 = 22.22\% \\ \text{Class VII} &= \left(\frac{35}{180}\right) \times 100 = 19.44\% \\ \text{Class VIII} &= \left(\frac{10}{180}\right) \times 100 = 5.56\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each percentage.
b) Monthly Budget of a Family:
The expenditure is:
- Food = Rs 2100
- Clothing = Rs 3300
- Miscellaneous = Rs 2250
- Saving = Rs 3150
Total Expenditure = 2100 + 3300 + 2250 + 3150 = Rs 10800
The percentages:
[tex]\[ \begin{array}{ll} \text{Food} &= \left(\frac{2100}{10800}\right) \times 100 = 19.44\% \\ \text{Clothing} &= \left(\frac{3300}{10800}\right) \times 100 = 30.56\% \\ \text{Miscellaneous} &= \left(\frac{2250}{10800}\right) \times 100 = 20.83\% \\ \text{Saving} &= \left(\frac{3150}{10800}\right) \times 100 = 29.17\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each category's percentage.
c) Mr. Limbu's Monthly Expenditure:
Total monthly expenditure is Rs 10,800. Breakdown:
- Food = Rs 2400
- Education = Rs 3600
- Rent = Rs 4200
- Miscellaneous = Rs 600
The percentages:
[tex]\[ \begin{array}{ll} \text{Food} &= \left(\frac{2400}{10800}\right) \times 100 = 22.22\% \\ \text{Education} &= \left(\frac{3600}{10800}\right) \times 100 = 33.33\% \\ \text{Rent} &= \left(\frac{4200}{10800}\right) \times 100 = 38.89\% \\ \text{Miscellaneous} &= \left(\frac{600}{10800}\right) \times 100 = 5.56\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each expenditure category's percentage.
d) Monthly Expenditure of a Family:
The table given is:
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \text{Item} & \text{Education} & \text{House rent} & \text{Food} & \text{Others} \\ \hline \text{Amount (Rs)} & 8000 & 4000 & 10000 & 14000 \\ \hline \end{array} \][/tex]
Total Expenditure = 8000 + 4000 + 10000 + 14000 = Rs 36000
The percentages:
[tex]\[ \begin{array}{ll} \text{Education} &= \left(\frac{8000}{36000}\right) \times 100 = 22.22\% \\ \text{House rent} &= \left(\frac{4000}{36000}\right) \times 100 = 11.11\% \\ \text{Food} &= \left(\frac{10000}{36000}\right) \times 100 = 27.78\% \\ \text{Others} &= \left(\frac{14000}{36000}\right) \times 100 = 38.89\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each expenditure category's percentage.
e) World Consumption of Energy:
The data is:
- Natural gas = 20%
- Nuclear = 5%
- Coal = 25%
- Hydroelectric = 10%
- Oil = 40%
To plot:
- Create a pie chart with sections representing each energy source's percentage.
For each pie chart, ensure the following:
- Title the pie chart appropriately.
- Use distinct color segments to differentiate categories.
- Label each segment with the corresponding percentage.
By following these steps, you can accurately depict the given data in pie charts.
a) Number of students from Class IV to VIII:
The table given is:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Class} & \text{IV} & \text{V} & \text{VI} & \text{VII} & \text{VIII} \\ \hline \text{No. of students} & 50 & 45 & 40 & 35 & 10 \\ \hline \end{array} \][/tex]
First, calculate the total number of students:
Total = 50 + 45 + 40 + 35 + 10 = 180
Next, compute the percentage of students in each class:
[tex]\[ \begin{array}{ll} \text{Class IV} &= \left(\frac{50}{180}\right) \times 100 = 27.78\% \\ \text{Class V} &= \left(\frac{45}{180}\right) \times 100 = 25.00\% \\ \text{Class VI} &= \left(\frac{40}{180}\right) \times 100 = 22.22\% \\ \text{Class VII} &= \left(\frac{35}{180}\right) \times 100 = 19.44\% \\ \text{Class VIII} &= \left(\frac{10}{180}\right) \times 100 = 5.56\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each percentage.
b) Monthly Budget of a Family:
The expenditure is:
- Food = Rs 2100
- Clothing = Rs 3300
- Miscellaneous = Rs 2250
- Saving = Rs 3150
Total Expenditure = 2100 + 3300 + 2250 + 3150 = Rs 10800
The percentages:
[tex]\[ \begin{array}{ll} \text{Food} &= \left(\frac{2100}{10800}\right) \times 100 = 19.44\% \\ \text{Clothing} &= \left(\frac{3300}{10800}\right) \times 100 = 30.56\% \\ \text{Miscellaneous} &= \left(\frac{2250}{10800}\right) \times 100 = 20.83\% \\ \text{Saving} &= \left(\frac{3150}{10800}\right) \times 100 = 29.17\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each category's percentage.
c) Mr. Limbu's Monthly Expenditure:
Total monthly expenditure is Rs 10,800. Breakdown:
- Food = Rs 2400
- Education = Rs 3600
- Rent = Rs 4200
- Miscellaneous = Rs 600
The percentages:
[tex]\[ \begin{array}{ll} \text{Food} &= \left(\frac{2400}{10800}\right) \times 100 = 22.22\% \\ \text{Education} &= \left(\frac{3600}{10800}\right) \times 100 = 33.33\% \\ \text{Rent} &= \left(\frac{4200}{10800}\right) \times 100 = 38.89\% \\ \text{Miscellaneous} &= \left(\frac{600}{10800}\right) \times 100 = 5.56\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each expenditure category's percentage.
d) Monthly Expenditure of a Family:
The table given is:
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \text{Item} & \text{Education} & \text{House rent} & \text{Food} & \text{Others} \\ \hline \text{Amount (Rs)} & 8000 & 4000 & 10000 & 14000 \\ \hline \end{array} \][/tex]
Total Expenditure = 8000 + 4000 + 10000 + 14000 = Rs 36000
The percentages:
[tex]\[ \begin{array}{ll} \text{Education} &= \left(\frac{8000}{36000}\right) \times 100 = 22.22\% \\ \text{House rent} &= \left(\frac{4000}{36000}\right) \times 100 = 11.11\% \\ \text{Food} &= \left(\frac{10000}{36000}\right) \times 100 = 27.78\% \\ \text{Others} &= \left(\frac{14000}{36000}\right) \times 100 = 38.89\% \end{array} \][/tex]
To plot:
- Create a pie chart with sections representing each expenditure category's percentage.
e) World Consumption of Energy:
The data is:
- Natural gas = 20%
- Nuclear = 5%
- Coal = 25%
- Hydroelectric = 10%
- Oil = 40%
To plot:
- Create a pie chart with sections representing each energy source's percentage.
For each pie chart, ensure the following:
- Title the pie chart appropriately.
- Use distinct color segments to differentiate categories.
- Label each segment with the corresponding percentage.
By following these steps, you can accurately depict the given data in pie charts.
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