Calculating Ratio of Average Male Populations

The question asks us to find the ratio of the average number of males in Town X to the average number of males in Town Y over the given five years, from 2018 to 2022. To do this, we first need to calculate the average number of males for each town.

The provided table gives the number of males and females (in thousands) for both towns across the five years. Let's extract the data for males in Town X and Town Y.

Step-by-Step Calculation of Average Males

Sum of Males in Town X

To find the average number of males in Town X, we sum the number of males for each year from 2018 to 2022 and then divide by the number of years, which is 5.

Sum of Males in Town X = Number of males in 2018 + 2019 + 2020 + 2021 + 2022

\begin{equation*} \text{Sum of Males in Town X} = 50 + 52 + 55 + 53 + 55 \end{equation*}

\begin{equation*} \text{Sum of Males in Town X} = 265 \text{ (in thousands)} \end{equation*}

Average Number of Males in Town X

Now, we calculate the average by dividing the sum by 5:

\begin{equation*} \text{Average Males in Town X} = \frac{\text{Sum of Males in Town X}}{\text{Number of Years}} \end{equation*}

\begin{equation*} \text{Average Males in Town X} = \frac{265}{5} \end{equation*}

\begin{equation*} \text{Average Males in Town X} = 53 \text{ (in thousands)} \end{equation*}

Sum of Males in Town Y

Next, we do the same for Town Y. Sum the number of males for each year from 2018 to 2022.

Sum of Males in Town Y = Number of males in 2018 + 2019 + 2020 + 2021 + 2022

\begin{equation*} \text{Sum of Males in Town Y} = 53 + 54 + 55 + 58 + 62 \end{equation*}

\begin{equation*} \text{Sum of Males in Town Y} = 282 \text{ (in thousands)} \end{equation*}

Average Number of Males in Town Y

Calculate the average by dividing the sum by 5:

\begin{equation*} \text{Average Males in Town Y} = \frac{\text{Sum of Males in Town Y}}{\text{Number of Years}} \end{equation*}

\begin{equation*} \text{Average Males in Town Y} = \frac{282}{5} \end{equation*}

\begin{equation*} \text{Average Males in Town Y} = 56.4 \text{ (in thousands)} \end{equation*}

Calculating the Ratio of Averages

The question asks for the ratio of the average number of males in Town X to the average number of males in Town Y.

Ratio = Average Males in Town X ∶ Average Males in Town Y

\begin{equation*} \text{Ratio} = \frac{265}{5} : \frac{282}{5} \end{equation*}

To express this ratio in its simplest integer form, we can multiply both parts of the ratio by the denominator, which is 5.

\begin{equation*} \text{Ratio} = \left(\frac{265}{5} \times 5\right) : \left(\frac{282}{5} \times 5\right) \end{equation*}

\begin{equation*} \text{Ratio} = 265 : 282 \end{equation*}

The ratio of the average number of males in Town X to the average number of males in Town Y is 265 ∶ 282.

Conclusion

Based on the calculations, the ratio of the average number of males in Town X to the average number of males in Town Y for the given period is 265 ∶ 282.

Revision Table - Average and Ratio Calculation

Additional Information - Data Interpretation Skills

Data interpretation questions often require extracting specific data points from tables, charts, or graphs and performing calculations like sums, averages, percentages, or ratios. Key skills include:

• Carefully reading the question to understand exactly what is being asked.
• Identifying the relevant data within the provided information source (e.g., rows and columns in a table).
• Performing calculations accurately.
• Presenting the final answer in the required format (e.g., as a ratio, percentage, or specific value).
• Understanding units (like 'thousands' in this case, although it didn't affect the final ratio).

Ratio problems involve comparing two quantities. A ratio $a:b$ can also be written as a fraction $\frac{a}{b}$. When comparing averages calculated over the same number of items (like years in this case), the ratio of the sums is equal to the ratio of the averages: $\frac{\text{Sum}_X}{\text{count}} : \frac{\text{Sum}_Y}{\text{count}} \implies \text{Sum}_X : \text{Sum}_Y$.