Analyzing Teacher Distribution Data

The question asks us to find the number of female teachers in City D as a percentage of the total number of teachers in City A. We are given a table showing the percentage distribution of the total 4500 teachers across six cities and the number of male teachers in each city.

Let's first present the given data in a structured format:

The total number of teachers in all six cities combined is 4500.

Step 1: Calculate the total number of teachers in City D

City D accounts for 15% of the total teachers. The total number of teachers is 4500.

Total teachers in City D = 15% of 4500

Using the percentage formula:

\begin{math} \text{Total teachers in City D} = \frac{15}{100} \times 4500 \end{math}

\begin{math} = 15 \times 45 \end{math}

\begin{math} = 675 \end{math}

So, there are 675 teachers in City D.

Step 2: Calculate the number of female teachers in City D

We know the total number of teachers in City D and the number of male teachers in City D.

Number of female teachers = Total teachers - Number of male teachers

Number of female teachers in City D = Total teachers in City D - Number of male teachers in City D

From the table, the number of male teachers in City D is 100.

Number of female teachers in City D = 675 - 100

Number of female teachers in City D = 575

Step 3: Calculate the total number of teachers in City A

City A accounts for 14% of the total teachers. The total number of teachers is 4500.

Total teachers in City A = 14% of 4500

Using the percentage formula:

\begin{math} \text{Total teachers in City A} = \frac{14}{100} \times 4500 \end{math}

\begin{math} = 14 \times 45 \end{math}

\begin{math} = 630 \end{math}

So, there are 630 teachers in City A.

Step 4: Calculate the percentage of female teachers in City D relative to total teachers in City A

We need to find what percentage the number of female teachers in City D (575) is of the total number of teachers in City A (630).

Required Percentage = \begin{math} \left( \frac{\text{Number of female teachers in City D}}{\text{Total number of teachers in City A}} \right) \times 100 \end{math}

Required Percentage = \begin{math} \left( \frac{575}{630} \right) \times 100 \end{math}

Let's perform the calculation:

\begin{math} \frac{575}{630} \approx 0.912698... \end{math}

Required Percentage \begin{math} \approx 0.912698... \times 100 \approx 91.27\% \end{math}

Rounding to the nearest whole number, the percentage is approximately 91%.

Summary of Calculations:

• Total teachers in City D: 675
• Female teachers in City D: 575
• Total teachers in City A: 630
• Percentage = \begin{math} \left( \frac{575}{630} \right) \times 100 \approx 91.27\% \end{math}

The value 91.27% is approximately 91%.

Based on our calculation, the number of female teachers in City D is approximately 91 percent of the total number of teachers in City A.

Revision Table: Key Data Points

Calculated Percentage: \begin{math} \left( \frac{\text{Female teachers in City D}}{\text{Total teachers in City A}} \right) \times 100 = \left( \frac{575}{630} \right) \times 100 \approx 91.27\% \end{math}

Additional Information on Data Interpretation

Data interpretation questions often require extracting information from tables, charts, or graphs and performing calculations based on that information. Key skills needed include:

• Reading and understanding the data presented.
• Calculating percentages, ratios, averages, and differences.
• Converting percentages to actual numbers and vice versa.
• Comparing values and quantities.
• Approximation techniques for quicker calculations, especially in exams.

In this specific problem, we used the percentage distribution to find the total number of teachers in specific cities and then used the given number of male teachers to find the number of female teachers. Finally, we calculated a percentage comparing values from two different cities.