Understanding Student Enrollment Data

The provided data table gives us information about the enrollment of students in different activities in a school during the 2020-21 session. We are given the total number of students enrolled and the total number of girls enrolled. We also have the percentage distribution of students and girls across five activities: Swimming, Singing, Drawing, Dancing, and Handicraft.

Let's first look at the key numbers provided:

• Total number of students enrolled = 3000
• Total number of girls enrolled = 1750

From these numbers, we can find the total number of boys enrolled:

Total number of boys = Total students - Total girls
Total number of boys = $3000 - 1750 = 1250$

Analyzing Swimming Activity Enrollment Data

The question asks for the ratio of the number of girls enrolled in Swimming to the number of boys enrolled in Swimming. To find this, we need to calculate the exact number of girls and boys enrolled specifically in the Swimming activity using the percentages given in the table.

Calculating the Number of Girls in Swimming

The table states that 14% of the total girls are enrolled in Swimming. The total number of girls is 1750.

Number of girls in Swimming = 14% of 1750
Number of girls in Swimming = $\frac{14}{100} \times 1750$
Number of girls in Swimming = $0.14 \times 1750 = 245$

So, 245 girls are enrolled in the Swimming activity.

Calculating the Total Number of Students in Swimming

The table states that 16% of the total students are enrolled in Swimming. The total number of students is 3000.

Total number of students in Swimming = 16% of 3000
Total number of students in Swimming = $\frac{16}{100} \times 3000$
Total number of students in Swimming = $0.16 \times 3000 = 480$

So, 480 students in total are enrolled in the Swimming activity. This total includes both girls and boys.

Calculating the Number of Boys in Swimming

Now that we know the total number of students in Swimming and the number of girls in Swimming, we can find the number of boys in Swimming.

Number of boys in Swimming = Total students in Swimming - Number of girls in Swimming
Number of boys in Swimming = $480 - 245 = 235$

So, 235 boys are enrolled in the Swimming activity.

Determining the Ratio of Girls to Boys in Swimming

We need to find the ratio of the number of girls enrolled in Swimming to the number of boys enrolled in Swimming.

Ratio = (Number of girls in Swimming) : (Number of boys in Swimming)
Ratio = $245 : 235$

To simplify this ratio, we can divide both numbers by their greatest common divisor. Both numbers are divisible by 5.

$245 \div 5 = 49$
$235 \div 5 = 47$

The simplified ratio is $49 : 47$.

Revision Table: Key Calculations for Enrollment Data

Additional Information: Ratio and Percentage Concepts

Ratio: A ratio is a comparison of two quantities. It shows how many times one quantity is contained in another. Ratios can be written using a colon ($a : b$), as a fraction ($\frac{a}{b}$), or with the word "to" ($a$ to $b$). When simplifying ratios, you divide both numbers by their greatest common divisor until they cannot be divided further by the same whole number (other than 1).

Percentage: A percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". To calculate a percentage of a number, you convert the percentage to a decimal (by dividing by 100) and then multiply it by the number. For example, 14% of 1750 is calculated as $0.14 \times 1750$.

This problem involves applying both percentage calculations to find the absolute numbers of girls and boys in a specific activity and then using these numbers to form and simplify a ratio. Data interpretation questions often require combining different mathematical concepts to arrive at the solution.