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Sagot :
To solve the given problem, we'll address parts (a) and (b) separately.
### (a) Represent the given data in a pie-chart
A pie chart is a circular graph divided into sectors, where each sector represents a proportional part of the whole. Here’s how you can create a pie chart based on the given data:
1. Collect the Data:
- Classes: VI, VII, VIII, IX, X
- Number of Students: 100, 150, 155, 135, 200
2. Calculate the Total Number of Students:
The total number of students is the sum of the students in all classes.
[tex]\[ \text{Total Students} = 100 + 150 + 155 + 135 + 200 = 740 \][/tex]
3. Calculate the Percentage of Students in Each Class:
- For Class VI:
[tex]\[ \text{Percentage} = \left(\frac{100}{740}\right) \times 100 \approx 13.51\% \][/tex]
- For Class VII:
[tex]\[ \text{Percentage} = \left(\frac{150}{740}\right) \times 100 \approx 20.27\% \][/tex]
- For Class VIII:
[tex]\[ \text{Percentage} = \left(\frac{155}{740}\right) \times 100 \approx 20.95\% \][/tex]
- For Class IX:
[tex]\[ \text{Percentage} = \left(\frac{135}{740}\right) \times 100 \approx 18.24\% \][/tex]
- For Class X:
[tex]\[ \text{Percentage} = \left(\frac{200}{740}\right) \times 100 \approx 27.03\% \][/tex]
Using these percentages, you can draw a pie chart where each sector represents the proportionate number of students in each class.
#### Example of Pie Chart Representation:
```plaintext
__________________________________________
/ [tex]$\ ____________ \ \$[/tex][tex]$\____ $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$_ 27.03% | \$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$ 200 - Class X | / $[/tex][tex]$$[/tex][tex]$$[/tex]____________ 13.51% /
[tex]$| $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex] 100 - Class VI /
[tex]$$[/tex][tex]$$[/tex][tex]$( $[/tex][tex]$ $[/tex][tex]$$ 20.27% / $[/tex][tex]$$[/tex] [tex]$$[/tex][tex]$$[/tex][tex]$ 155 - Class VIII | $[/tex][tex]$$[/tex] [tex]$$[/tex][tex]$$[/tex][tex]$ /20.95% / $[/tex][tex]$$ $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$ 150 - Class VII| $[/tex][tex]$ $[/tex][tex]$$____________ 18.24% / | $[/tex][tex]$[/tex] 135 - Class IX \________/
```
### (b) Find the average number of students per class from class VI to class X
The average number of students per class can be found by dividing the total number of students by the number of classes.
1. Number of Classes:
There are 5 classes (VI, VII, VIII, IX, and X).
2. Total Number of Students:
As we calculated earlier, the total number of students is 740.
3. Calculate the Average:
[tex]\[ \text{Average number of students per class} = \frac{\text{Total Students}}{\text{Number of Classes}} \][/tex]
[tex]\[ \text{Average number of students per class} = \frac{740}{5} = 148 \][/tex]
So, the average number of students per class from class VI to class X is 148.
### Summary:
(a) We represented the number of students in each class using a pie chart, calculating the proportional percentage of each class.
(b) We found that the average number of students per class is 148.
### (a) Represent the given data in a pie-chart
A pie chart is a circular graph divided into sectors, where each sector represents a proportional part of the whole. Here’s how you can create a pie chart based on the given data:
1. Collect the Data:
- Classes: VI, VII, VIII, IX, X
- Number of Students: 100, 150, 155, 135, 200
2. Calculate the Total Number of Students:
The total number of students is the sum of the students in all classes.
[tex]\[ \text{Total Students} = 100 + 150 + 155 + 135 + 200 = 740 \][/tex]
3. Calculate the Percentage of Students in Each Class:
- For Class VI:
[tex]\[ \text{Percentage} = \left(\frac{100}{740}\right) \times 100 \approx 13.51\% \][/tex]
- For Class VII:
[tex]\[ \text{Percentage} = \left(\frac{150}{740}\right) \times 100 \approx 20.27\% \][/tex]
- For Class VIII:
[tex]\[ \text{Percentage} = \left(\frac{155}{740}\right) \times 100 \approx 20.95\% \][/tex]
- For Class IX:
[tex]\[ \text{Percentage} = \left(\frac{135}{740}\right) \times 100 \approx 18.24\% \][/tex]
- For Class X:
[tex]\[ \text{Percentage} = \left(\frac{200}{740}\right) \times 100 \approx 27.03\% \][/tex]
Using these percentages, you can draw a pie chart where each sector represents the proportionate number of students in each class.
#### Example of Pie Chart Representation:
```plaintext
__________________________________________
/ [tex]$\ ____________ \ \$[/tex][tex]$\____ $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$_ 27.03% | \$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex][tex]$ 200 - Class X | / $[/tex][tex]$$[/tex][tex]$$[/tex]____________ 13.51% /
[tex]$| $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$$[/tex] 100 - Class VI /
[tex]$$[/tex][tex]$$[/tex][tex]$( $[/tex][tex]$ $[/tex][tex]$$ 20.27% / $[/tex][tex]$$[/tex] [tex]$$[/tex][tex]$$[/tex][tex]$ 155 - Class VIII | $[/tex][tex]$$[/tex] [tex]$$[/tex][tex]$$[/tex][tex]$ /20.95% / $[/tex][tex]$$ $[/tex][tex]$$[/tex][tex]$$[/tex][tex]$ 150 - Class VII| $[/tex][tex]$ $[/tex][tex]$$____________ 18.24% / | $[/tex][tex]$[/tex] 135 - Class IX \________/
```
### (b) Find the average number of students per class from class VI to class X
The average number of students per class can be found by dividing the total number of students by the number of classes.
1. Number of Classes:
There are 5 classes (VI, VII, VIII, IX, and X).
2. Total Number of Students:
As we calculated earlier, the total number of students is 740.
3. Calculate the Average:
[tex]\[ \text{Average number of students per class} = \frac{\text{Total Students}}{\text{Number of Classes}} \][/tex]
[tex]\[ \text{Average number of students per class} = \frac{740}{5} = 148 \][/tex]
So, the average number of students per class from class VI to class X is 148.
### Summary:
(a) We represented the number of students in each class using a pie chart, calculating the proportional percentage of each class.
(b) We found that the average number of students per class is 148.
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