In two successive tests a student gains marks of 57/79 and 49/67. Is the second mark better or worse than the first?
Place the following in order of size, the smallest first, expressing each as a percentage correct to 1 decimal place.
(a) (b) (c) (d)
The Correct Answer and Explanation is :
To compare the two marks, we need to calculate each as a percentage and compare their values. Let’s calculate:
- First Test:
Marks scored = 57
Total marks = 79
Percentage = ( \frac{57}{79} \times 100 = 72.2\% ) (to 1 decimal place). - Second Test:
Marks scored = 49
Total marks = 67
Percentage = ( \frac{49}{67} \times 100 = 73.1\% ) (to 1 decimal place).
Comparison:
The second mark (73.1%) is better than the first mark (72.2%) because it represents a higher percentage score.
Ordering Percentages:
Let’s evaluate and rank the following options in ascending order, expressing them to 1 decimal place:
(a) ( \frac{24}{33} \times 100 = 72.7\% )
(b) ( \frac{13}{20} \times 100 = 65.0\% )
(c) ( \frac{18}{25} \times 100 = 72.0\% )
(d) ( \frac{45}{61} \times 100 = 73.8\% )
Ordered Percentages:
(b) 65.0%, (c) 72.0%, (a) 72.7%, (d) 73.8%.
Explanation:
The percentages allow us to compare scores across tests or data points with different total marks, providing a fair metric. The percentage calculation standardizes the data by scaling the scores relative to the total possible marks. In the first part of the question, the second test was better because its percentage (73.1%) exceeded the first (72.2%).
In the second part, the percentages for (a), (b), (c), and (d) were calculated, rounded to 1 decimal place, and ranked in ascending order. The lowest percentage (65.0%) belongs to (b), followed by (c) (72.0%), (a) (72.7%), and finally the highest (d) (73.8%).
Understanding and comparing percentages is an essential skill, especially in exams, financial data, or performance metrics, where relative comparison matters more than absolute values.