Understanding the Common Entrance Test (CET) Data for 2021

This question asks for the average number of female candidates who qualified the Common Entrance Test (CET) across six different cities (A, B, C, D, E, and F) in the year 2021. We are given the total number of qualified candidates in 2021, the percentage distribution of these candidates across the six cities, and the ratio of male to female qualified candidates within each city for that year.

The total number of qualified candidates in all six cities together during 2021 is 4600.

Calculating Female Qualified Candidates per City in 2021

To find the average number of female qualified candidates, we first need to calculate the number of qualified female candidates in each city for the year 2021. We can do this by using the distribution percentage and the male to female ratio provided in the table for 2021.

Here’s the breakdown for each city:

• City A:
  • Distribution % = 24%
  • Ratio (Male : Female) = 5 : 7
  • Total Qualified Candidates in A = $\text{4600} \times \frac{24}{100} = \text{46} \times \text{24} = \text{1104}$
  • Total ratio parts = $\text{5} + \text{7} = \text{12}$
  • Number of Females in A = $\text{1104} \times \frac{7}{12} = \text{92} \times \text{7} = \text{644}$
• City B:
  • Distribution % = 15%
  • Ratio (Male : Female) = 12 : 11
  • Total Qualified Candidates in B = $\text{4600} \times \frac{15}{100} = \text{46} \times \text{15} = \text{690}$
  • Total ratio parts = $\text{12} + \text{11} = \text{23}$
  • Number of Females in B = $\text{690} \times \frac{11}{23} = \text{30} \times \text{11} = \text{330}$
• City C:
  • Distribution % = 23%
  • Ratio (Male : Female) = 15 : 8
  • Total Qualified Candidates in C = $\text{4600} \times \frac{23}{100} = \text{46} \times \text{23} = \text{1058}$
  • Total ratio parts = $\text{15} + \text{8} = \text{23}$
  • Number of Females in C = $\text{1058} \times \frac{8}{23} = \text{46} \times \text{8} = \text{368}$
• City D:
  • Distribution % = 17%
  • Ratio (Male : Female) = 8 : 9
  • Total Qualified Candidates in D = $\text{4600} \times \frac{17}{100} = \text{46} \times \text{17} = \text{782}$
  • Total ratio parts = $\text{8} + \text{9} = \text{17}$
  • Number of Females in D = $\text{782} \times \frac{9}{17} = \text{46} \times \text{9} = \text{414}$
• City E:
  • Distribution % = 8%
  • Ratio (Male : Female) = 1 : 3
  • Total Qualified Candidates in E = $\text{4600} \times \frac{8}{100} = \text{46} \times \text{8} = \text{368}$
  • Total ratio parts = $\text{1} + \text{3} = \text{4}$
  • Number of Females in E = $\text{368} \times \frac{3}{4} = \text{92} \times \text{3} = \text{276}$
• City F:
  • Distribution % = 13%
  • Ratio (Male : Female) = 5 : 8
  • Total Qualified Candidates in F = $\text{4600} \times \frac{13}{100} = \text{46} \times \text{13} = \text{598}$
  • Total ratio parts = $\text{5} + \text{8} = \text{13}$
  • Number of Females in F = $\text{598} \times \frac{8}{13} = \text{46} \times \text{8} = \text{368}$

Summary of Female Qualified Candidates in 2021

Let's list the number of female qualified candidates we calculated for each city in 2021:

Calculating the Average Number of Female Qualified Candidates

Now, we need to find the total number of female qualified candidates from all six cities in 2021 and then calculate their average.

Total number of female qualified candidates = Sum of females from cities A, B, C, D, E, F

Total Females = $\text{644} + \text{330} + \text{368} + \text{414} + \text{276} + \text{368} = \text{2400}$

The average number of female qualified candidates is the total number of females divided by the number of cities (which is 6).

Average Females = $\frac{\text{Total Females}}{\text{Number of Cities}} = \frac{2400}{6} = 400$

Conclusion on CET Qualified Females Average

The average number of females found qualified from all the six cities in the year 2021 is 400.

Revision Table: CET Data Analysis 2021

This table summarizes the calculated values for female qualified candidates per city in 2021.

Additional Information: Understanding Ratios and Percentages

Data interpretation questions often involve using percentages and ratios to extract specific information from a dataset.

• Percentage: A percentage represents a part of a whole, expressed as a fraction of 100. For example, 24% of 4600 means $\frac{24}{100} \times 4600$.
• Ratio: A ratio shows the relationship between two or more quantities. A ratio of M:F means that for every M parts of one quantity, there are F parts of another. To find the value of one part when the total is known, you sum the ratio parts (M+F) and divide the total by this sum. Then multiply by the respective part of the ratio. For example, in a 5:7 ratio, the total parts are 12. If the total is 1104, one part is $1104/12=92$. The number corresponding to the '7' part is $7 \times 92 = 644$.
• Average: The average (or mean) is calculated by summing all the values in a set and dividing by the number of values in the set. In this case, we sum the number of females in each city and divide by the number of cities (6).

Mastering these concepts is crucial for solving data interpretation problems based on tables and charts.