Analysing State Population Data

The question asks us to determine which state among A, B, C, D, and E has the highest number of female residents in the Graduate category, assuming each state has a total population of 1 million. We need to use the data provided in the table to calculate the number of female graduates for each state.

Interpreting the Data Table

The provided table presents information about the population distribution by education level and sex for five states. The headers and data points require careful interpretation to extract the necessary information. We will interpret the table as follows:

• The 'Percentage of Educated Population' column gives the overall percentage of people who are educated in each state.
• The numbers under '(10+2 Category)' and '(Graduate Category)' represent parts in a ratio that divides the total educated population into these two categories. For example, in State A, the ratio of 10+2 educated to Graduates within the educated population is 5:65.
• The numbers under 'Proportion of Males and Females' represent parts in a ratio that divides the population within a specific education category by sex. Given the question focuses on 'female population (in the Graduate category)' and the numbers in this ratio align with the '10+2 Category' and 'Graduate Category' columns, we will interpret the first number in the ratio as the proportion of Males among Graduates and the second number as the proportion of Females among Graduates. The third number in the ratio appears extraneous for this specific calculation.

Step-by-Step Calculation for Each State

For each state, we will follow these steps to calculate the number of female graduates:

1. Calculate the total educated population in the state.
2. Calculate the number of graduates within the educated population based on the 10+2:Graduate ratio.
3. Calculate the number of female graduates within the graduate population based on the Male:Female graduate ratio.

Let's perform the calculations for each state, assuming a total population of $\text{1,000,000}$ for each.

State A

• Total Population: $\text{1,000,000}$
• Percentage of Educated Population: $\text{60%}$
• Total Educated Population: $\text{1,000,000} \times \frac{60}{100} = \text{600,000}$
• Ratio of 10+2 to Graduates within Educated: $\text{5 : 65}$. Total parts: $\text{5 + 65 = 70}$.
• Proportion of Graduates within Educated: $\frac{65}{70}$
• Number of Graduates: $\text{600,000} \times \frac{65}{70} = \text{600,000} \times \frac{13}{14} \approx \text{557,142.86}$
• Ratio of Male to Female among Graduates: $\text{5 : 65}$. Total parts: $\text{5 + 65 = 70}$.
• Proportion of Female among Graduates: $\frac{65}{70}$
• Number of Female Graduates in State A: $\left(\text{1,000,000} \times \frac{60}{100}\right) \times \left(\frac{65}{5+65}\right) \times \left(\frac{65}{5+65}\right) = \text{1,000,000} \times \text{0.60} \times \frac{65}{70} \times \frac{65}{70} = \text{600,000} \times \left(\frac{65}{70}\right)^2$
• Number of Female Graduates in State A: $\text{600,000} \times \left(\frac{13}{14}\right)^2 = \text{600,000} \times \frac{169}{196} = \frac{101,400,000}{196} = \frac{25,350,000}{49} \approx \text{517,347}$

State B

• Total Population: $\text{1,000,000}$
• Percentage of Educated Population: $\text{50%}$
• Total Educated Population: $\text{1,000,000} \times \frac{50}{100} = \text{500,000}$
• Ratio of 10+2 to Graduates within Educated: $\text{5 : 55}$. Total parts: $\text{5 + 55 = 60}$.
• Proportion of Graduates within Educated: $\frac{55}{60}$
• Ratio of Male to Female among Graduates: $\text{5 : 55}$. Total parts: $\text{5 + 55 = 60}$.
• Proportion of Female among Graduates: $\frac{55}{60}$
• Number of Female Graduates in State B: $\left(\text{1,000,000} \times \frac{50}{100}\right) \times \left(\frac{55}{5+55}\right) \times \left(\frac{55}{5+55}\right) = \text{1,000,000} \times \text{0.50} \times \frac{55}{60} \times \frac{55}{60} = \text{500,000} \times \left(\frac{55}{60}\right)^2$
• Number of Female Graduates in State B: $\text{500,000} \times \left(\frac{11}{12}\right)^2 = \text{500,000} \times \frac{121}{144} = \frac{60,500,000}{144} \approx \text{420,139}$

State C

• Total Population: $\text{1,000,000}$
• Percentage of Educated Population: $\text{35%}$
• Total Educated Population: $\text{1,000,000} \times \frac{35}{100} = \text{350,000}$
• Ratio of 10+2 to Graduates within Educated: $\text{5 : 34}$. Total parts: $\text{5 + 34 = 39}$.
• Proportion of Graduates within Educated: $\frac{34}{39}$
• Ratio of Male to Female among Graduates: $\text{5 : 34}$. Total parts: $\text{5 + 34 = 39}$.
• Proportion of Female among Graduates: $\frac{34}{39}$
• Number of Female Graduates in State C: $\left(\text{1,000,000} \times \frac{35}{100}\right) \times \left(\frac{34}{5+34}\right) \times \left(\frac{34}{5+34}\right) = \text{1,000,000} \times \text{0.35} \times \frac{34}{39} \times \frac{34}{39} = \text{350,000} \times \left(\frac{34}{39}\right)^2$
• Number of Female Graduates in State C: $\text{350,000} \times \frac{1156}{1521} = \frac{404,600,000}{1521} \approx \text{266,009}$

State D

• Total Population: $\text{1,000,000}$
• Percentage of Educated Population: $\text{45%}$
• Total Educated Population: $\text{1,000,000} \times \frac{45}{100} = \text{450,000}$
• Ratio of 10+2 to Graduates within Educated: $\text{6 : 54}$. Total parts: $\text{6 + 54 = 60}$.
• Proportion of Graduates within Educated: $\frac{54}{60} = \frac{9}{10}$
• Ratio of Male to Female among Graduates: $\text{6 : 54}$. Total parts: $\text{6 + 54 = 60}$.
• Proportion of Female among Graduates: $\frac{54}{60} = \frac{9}{10}$
• Number of Female Graduates in State D: $\left(\text{1,000,000} \times \frac{45}{100}\right) \times \left(\frac{54}{6+54}\right) \times \left(\frac{54}{6+54}\right) = \text{1,000,000} \times \text{0.45} \times \frac{54}{60} \times \frac{54}{60} = \text{450,000} \times \left(\frac{9}{10}\right)^2$
• Number of Female Graduates in State D: $\text{450,000} \times \frac{81}{100} = \text{4500} \times 81 = \text{364,500}$

State E

• Total Population: $\text{1,000,000}$
• Percentage of Educated Population: $\text{41%}$
• Total Educated Population: $\text{1,000,000} \times \frac{41}{100} = \text{410,000}$
• Ratio of 10+2 to Graduates within Educated: $\text{4 : 33}$. Total parts: $\text{4 + 33 = 37}$.
• Proportion of Graduates within Educated: $\frac{33}{37}$
• Ratio of Male to Female among Graduates: $\text{4 : 33}$. Total parts: $\text{4 + 33 = 37}$.
• Proportion of Female among Graduates: $\frac{33}{37}$
• Number of Female Graduates in State E: $\left(\text{1,000,000} \times \frac{41}{100}\right) \times \left(\frac{33}{4+33}\right) \times \left(\frac{33}{4+33}\right) = \text{1,000,000} \times \text{0.41} \times \frac{33}{37} \times \frac{33}{37} = \text{410,000} \times \left(\frac{33}{37}\right)^2$
• Number of Female Graduates in State E: $\text{410,000} \times \frac{1089}{1369} = \frac{446,490,000}{1369} \approx \text{326,143}$

Comparison of Female Graduate Numbers

Let's compare the approximate number of female graduates for each state:

• State A: $\text{517,347}$
• State B: $\text{420,139}$
• State C: $\text{266,009}$
• State D: $\text{364,500}$
• State E: $\text{326,143}$

Comparing these numbers, State A has the highest number of female graduates.

Conclusion

Based on the calculations using the provided data and our interpretation of the table structure, State A will have the highest number of female population in the Graduate category.

Revision Table for Data Interpretation Practice

When tackling data interpretation questions involving tables and distributions, consider the following:

• Always read the table title and column headers carefully.
• Understand what percentages or ratios represent (e.g., percentage of total population, percentage of a subgroup, ratio of parts).
• Pay close attention to how different columns relate to each other.
• Break down the required calculation into smaller steps.
• Be consistent with your interpretation across all categories or states.
• Double-check calculations, especially when dealing with multiple proportions or percentages.

Additional Information on Population Data Analysis

Population data analysis often involves looking at distributions across various categories like age, sex, education level, occupation, etc. Such analysis helps in understanding demographic trends, planning resources, and formulating policies. Data can be presented in tables, charts, or graphs, and interpreting this data requires careful reading and calculation skills. Questions often test the ability to extract specific information from complex data presentations and perform calculations based on percentages, ratios, and proportions.