The question asks for the percentage of candidates who passed the Ph.D. entrance exam from Institute F, calculated with respect to the total number of candidates who were enrolled in Institute F.

We are given the following information:

• Total number of candidates enrolled for the exam across all institutes: 17100
• Total number of candidates who passed the exam across all institutes: 11400
• A table showing the percentage distribution of enrolled and passed candidates for each institute (A-G).

Let's look at the data for Institute F from the table.

From the table, for Institute F:

• Percentage of enrolled candidates in F = 8% of the total enrolled (17100)
• Percentage of passed candidates in F = 9% of the total passed (11400)

First, we need to calculate the actual number of candidates enrolled in Institute F:

Number of candidates enrolled in F = 8% of 17100

Number of candidates enrolled in F = $\frac{8}{100} \times 17100 = 8 \times 171 = 1368$

Next, we need to calculate the actual number of candidates who passed the exam from Institute F:

Number of candidates passed in F = 9% of 11400

Number of candidates passed in F = $\frac{9}{100} \times 11400 = 9 \times 114 = 1026$

The question asks for the percentage of candidates who passed from Institute F out of the total number of candidates enrolled in F. This means we need to calculate the pass percentage specifically for Institute F based on its own enrolled candidates.

Percentage of candidates passed in F out of total enrolled in F = $\left( \frac{\text{Number of candidates passed in F}}{\text{Number of candidates enrolled in F}} \right) \times 100\%$

Percentage = $\left( \frac{1026}{1368} \right) \times 100\%$

Now, let's simplify the fraction $\frac{1026}{1368}$. Both numbers are divisible by 2:

$\frac{1026 \div 2}{1368 \div 2} = \frac{513}{684}$

Both 513 and 684 are divisible by 9 (sum of digits 5+1+3=9, 6+8+4=18):

$\frac{513 \div 9}{684 \div 9} = \frac{57}{76}$

Both 57 and 76 are divisible by 19 (since $57 = 3 \times 19$ and $76 = 4 \times 19$):

$\frac{57 \div 19}{76 \div 19} = \frac{3}{4}$

So, the fraction is $\frac{3}{4}$. Now, calculate the percentage:

Percentage = $\frac{3}{4} \times 100\% = 0.75 \times 100\% = 75\%$

Therefore, 75% of the candidates enrolled in Institute F passed the exam.

Revision Table: Ph.D. Entrance Exam Data Analysis

Understanding the different percentages is key in data interpretation questions like this. Here's a quick summary of the calculations for Institute F:

• Total Enrolled: 17100
• Total Passed: 11400
• Enrolled in F: 8% of 17100 = 1368
• Passed in F: 9% of 11400 = 1026
• Pass Percentage for F (out of Enrolled in F): (1026 / 1368) * 100% = 75%

Additional Information: Data Interpretation Concepts

Data interpretation questions often involve calculating different types of percentages or averages based on provided tables or charts. It's important to carefully read what the percentage is relative to (e.g., percentage of passed out of total enrolled, percentage passed out of enrolled in a specific institute, percentage distribution out of total passed). In this case, the key was to calculate the pass rate *within* Institute F.

• Percentage Distribution: Shows how a total quantity is divided among different categories, expressed as percentages of the total.
• Calculating Actual Values: When given a total and a percentage distribution, you can find the actual value for a category by multiplying the total by the percentage (as a decimal).
• Calculating Relative Percentage: Sometimes you need to find the percentage of one value relative to another specific value (not necessarily the overall total), as demonstrated in this problem. The formula is $\left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\%$.

Practice with different types of data representation (tables, bar graphs, pie charts) and percentage calculations will help you solve such problems efficiently.