Calculating City Population Percentage Using Distribution Data

This problem requires us to use the provided table data on city population distribution to find the population of one city as a percentage of another. We are given the percentage distribution of the total population across six cities (A-F) and the actual population of City A.

Here is the data presented in the table:

We are given that the population of City A is 257400.

From the table, City A represents 23.4% of the total population. City D represents 18.9% of the total population.

Steps to Compare Population of City A and City D

To find the population of City A as a percentage of the population of City D, we can use the percentage distribution values directly because both are percentages of the same total population. Let's assume the total population is 'P'.

• Population of City A = 23.4% of P = $0.234 \times P$
• Population of City D = 18.9% of P = $0.189 \times P$

The percentage of Population of City A relative to Population of City D is calculated as:

$\left( \frac{\text{Population of City A}}{\text{Population of City D}} \right) \times 100\%$

Substituting the expressions in terms of the total population 'P':

$\left( \frac{0.234 \times P}{0.189 \times P} \right) \times 100\%$

Notice that 'P' cancels out from the numerator and denominator. So, we only need the percentage distribution values:

$\left( \frac{0.234}{0.189} \right) \times 100\%$

Performing the Percentage Calculation

Now, let's calculate the value:

$\frac{0.234}{0.189} \approx 1.238095$

Multiply by 100 to get the percentage:

$1.238095 \times 100\% \approx 123.81\%$

Approximating the Result

The question asks for the approximate percentage. The calculated value, 123.81%, is closest to 124% among the given options.

Alternatively, using the exact population of City A (257400) to find the total population and then City D's population:

• Let Total Population be T.
• $23.4\%$ of T = 257400
• $T = \frac{257400}{0.234} \approx 1100000$
• Population of City D = $18.9\%$ of T = $0.189 \times 1100000 = 207900$
• Percentage = $\left( \frac{\text{Population of City A}}{\text{Population of City D}} \right) \times 100\% = \left( \frac{257400}{207900} \right) \times 100\%$
• $\frac{257400}{207900} \approx 1.2380957...$
• $1.2380957... \times 100\% \approx 123.81\%$

Both methods give the same approximate result, 123.81%, which is approximately 124%.

Revision Table: Key Concepts for Population Data

Additional Information on Data Interpretation

Data interpretation questions often involve tables, charts, or graphs presenting statistical data. Success in these questions depends on carefully reading the information provided, understanding what is being asked, and applying basic mathematical concepts like percentages, ratios, averages, and proportions.

• Always pay attention to the units or what the percentages represent (e.g., percentage of total population, percentage of adults within a city).
• Understand the relationship between different data points. In this case, the percentage distributions of cities A and D are both relative to the same total population.
• Approximation is often required in multiple-choice questions, so practice rounding and estimating.
• Break down complex problems into smaller, manageable steps.

This problem highlights how understanding percentage relationships is key to solving data interpretation questions involving population distribution.