Answer :
We start by converting each score into a percentage. For a score given as "[tex]$\text{score out of total}$[/tex]," the percentage is calculated by
[tex]$$
\text{Percentage} = \left(\frac{\text{score}}{\text{total}}\right) \times 100.
$$[/tex]
Following this procedure for each pair, we obtain the following percentages:
1. [tex]$\frac{48}{50} \times 100 = 96\%$[/tex]
2. [tex]$\frac{49}{50} \times 100 = 98\%$[/tex]
3. [tex]$\frac{46}{50} \times 100 = 92\%$[/tex]
4. [tex]$\frac{46}{50} \times 100 = 92\%$[/tex]
5. [tex]$\frac{45}{50} \times 100 = 90\%$[/tex]
6. [tex]$\frac{45}{50} \times 100 = 90\%$[/tex]
7. [tex]$\frac{47}{50} \times 100 = 94\%$[/tex]
8. [tex]$\frac{47}{50} \times 100 = 94\%$[/tex]
9. [tex]$\frac{48}{50} \times 100 = 96\%$[/tex]
10. [tex]$\frac{20}{25} \times 100 = 80\%$[/tex]
11. [tex]$\frac{76}{80} \times 100 = 95\%$[/tex]
12. [tex]$\frac{72}{80} \times 100 = 90\%$[/tex]
13. [tex]$\frac{70}{80} \times 100 = 87.5\%$[/tex]
14. [tex]$\frac{40}{80} \times 100 = 50\%$[/tex]
15. [tex]$\frac{70}{80} \times 100 = 87.5\%$[/tex]
Next, we sum these individual percentages:
[tex]$$
\text{Total percentage} = 96 + 98 + 92 + 92 + 90 + 90 + 94 + 94 + 96 + 80 + 95 + 90 + 87.5 + 50 + 87.5 = 1332.
$$[/tex]
Since there are 15 scores, the average percentage is calculated by dividing the total percentage by 15:
[tex]$$
\text{Average percentage} = \frac{1332}{15} = 88.8\%.
$$[/tex]
Thus, the detailed steps lead us to conclude that the average percentage for the given scores is [tex]$88.8\%$[/tex].
[tex]$$
\text{Percentage} = \left(\frac{\text{score}}{\text{total}}\right) \times 100.
$$[/tex]
Following this procedure for each pair, we obtain the following percentages:
1. [tex]$\frac{48}{50} \times 100 = 96\%$[/tex]
2. [tex]$\frac{49}{50} \times 100 = 98\%$[/tex]
3. [tex]$\frac{46}{50} \times 100 = 92\%$[/tex]
4. [tex]$\frac{46}{50} \times 100 = 92\%$[/tex]
5. [tex]$\frac{45}{50} \times 100 = 90\%$[/tex]
6. [tex]$\frac{45}{50} \times 100 = 90\%$[/tex]
7. [tex]$\frac{47}{50} \times 100 = 94\%$[/tex]
8. [tex]$\frac{47}{50} \times 100 = 94\%$[/tex]
9. [tex]$\frac{48}{50} \times 100 = 96\%$[/tex]
10. [tex]$\frac{20}{25} \times 100 = 80\%$[/tex]
11. [tex]$\frac{76}{80} \times 100 = 95\%$[/tex]
12. [tex]$\frac{72}{80} \times 100 = 90\%$[/tex]
13. [tex]$\frac{70}{80} \times 100 = 87.5\%$[/tex]
14. [tex]$\frac{40}{80} \times 100 = 50\%$[/tex]
15. [tex]$\frac{70}{80} \times 100 = 87.5\%$[/tex]
Next, we sum these individual percentages:
[tex]$$
\text{Total percentage} = 96 + 98 + 92 + 92 + 90 + 90 + 94 + 94 + 96 + 80 + 95 + 90 + 87.5 + 50 + 87.5 = 1332.
$$[/tex]
Since there are 15 scores, the average percentage is calculated by dividing the total percentage by 15:
[tex]$$
\text{Average percentage} = \frac{1332}{15} = 88.8\%.
$$[/tex]
Thus, the detailed steps lead us to conclude that the average percentage for the given scores is [tex]$88.8\%$[/tex].