To determine which scale Gemma should use for the vertical axis of the histogram to maximize the difference in the heights of the bars, let's first analyze the given data:
The table shows the number of people in each salary range:
- [tex]$0-$[/tex]19,999: 40 people
- [tex]$20,000-$[/tex]39,999: 30 people
- [tex]$40,000-$[/tex]59,999: 35 people
We need to assess the values and determine which suggested scales will maximize the difference in bar heights.
1. 0-50: This range encompasses all the values from 0 to 40. This will show the full range of the data (0 to 40) and provide a proportional representation of each group's height.
2. 0-40: This range would also encompass the data points from 0 to 40. However, since 40 is the maximum value, the top bar (for [tex]$0-$[/tex]19,999) would touch the upper limit of the scale. This might not provide as clear a visual difference between the bars since one bar already hits the limit.
3. 10-50: This range starts at 10, which means the first part of the range (0-10) is not represented, effectively compressing the height differences, which will skew the visual representation negatively and compress the lower bars close together.
4. [tex]$25-40$[/tex]: This range is quite narrow and does not encompass lower data points (0 to 24). This would exclude some of the data entirely and severely skew the representation, as only part of the data from 25 to 40 would be shown.
The best scale to use, which encompasses all the data points while providing the clearest visual differentiation between the bar heights, allowing the differences to be visually prominent, is the 0-50 scale. This option maximizes the difference in heights as all relevant data points are within this range without compressing lower values significantly.
Therefore, Gemma should use the 0-50 scale for the vertical axis to maximize the difference in heights of the histogram bars.
