To determine the most suitable scale for the vertical axis so that the differences in the heights of the bars are maximized, we'll proceed step by step.
1. Identify the maximum number of people across all salary ranges:
- For the [tex]$0-$[/tex]19,999 range, there are 40 people.
- For the [tex]$20,000-$[/tex]39,999 range, there are 30 people.
- For the [tex]$40,000-$[/tex]59,999 range, there are 35 people.
The maximum number of people in any salary range is 40.
2. Review the available scale options:
- The scales provided are 0-50, 0-40, 10-50, and 25-40.
3. Determine the smallest suitable scale:
- The chosen scale must be high enough to include the maximum value of 40.
- The scales 0-50, 0-40, and 10-50 can accommodate 40.
- The scale 25-40 starts at 25, but it accommodates up to 40 as well.
4. Select the scale that maximizes the differences in bar heights:
- The scale 0-50 provides a range that goes much higher than the maximum of 40, leaving room above the highest bar and thus diminishing comparative differences.
- The scale 10-50 starts at 10, thus not using the full range of comparison properly.
- The scale 0-40 fits the maximum value exactly and allows the total range to be used effectively. Since it's just enough to accommodate 40, it optimally highlights the differences between the heights of the bars.
- The scale 25-40, although accommodating 40, doesn't start from zero which is unconventional for histograms and does not provide a clear visual representation of lower ranges starting from zero.
Given this analysis, the best choice for maximizing the visual differences in bar heights is:
Scale: 0-50.
