which graphical representation would be most useful in comparing the change in average earning of male employees versus average earning of female employees over the course of a 50 year period?

I'd use a line graph.

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To compare the change in average earnings of male employees versus female employees over a 50-year period, a line graph would be the most useful graphical representation.

Here's how you could create a line graph to visualize this comparison:

1. Gather the necessary data: Collect the average earnings data for male employees and female employees for each year over the 50-year period. Make sure you have a data set representing the average earnings for both genders separately.

2. Choose the axes: Select the horizontal (X) axis to represent the 50-year period, typically with each year marked along the axis. Choose the vertical (Y) axis to represent the average earnings, with appropriate increments based on the data range.

3. Plot the data points: For each year, plot the average earnings of male employees as one data point and the average earnings of female employees as another data point. The X-coordinate would be the corresponding year, and the Y-coordinate would be the average earnings for that specific year.

4. Connect the points with lines: Once all the data points are plotted, connect them with separate lines for male and female employees. This will represent the trend of average earnings over the 50-year period for each gender.

5. Add labels and titles: Label the axes with appropriate titles (e.g., "Year" for the X-axis and "Average Earnings" for the Y-axis). Add a clear, descriptive title for the graph itself, such as "Comparison of Average Earnings: Male vs. Female Employees over 50 Years."

6. Enhance the graph (optional): You can further enhance the graph by adding a legend or color-coding the lines to differentiate between male and female employees easily.

By creating a line graph, you can visually compare the change in average earnings of male and female employees over the 50-year period. This representation allows for easy observation of trends, patterns, and any significant differences between the two genders' average earning trajectories.