To determine the best scale for the vertical axis of the histogram that maximizes the difference in the heights of the bars, let's analyze the problem step-by-step.
1. Identify 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
2. Find the maximum number of people in any salary range:
- The maximum number is 40 people.
3. Define the scales to evaluate:
- Scale 1: 0 to 50
- Scale 2: 0 to 40
- Scale 3: 10 to 50
- Scale 4: 25 to 40
4. Calculate the difference between the maximum value and the minimum value for each scale:
- Scale 1: [tex]\( 50 - 0 = 50 \)[/tex]
- Scale 2: [tex]\( 40 - 0 = 40 \)[/tex]
- Scale 3: [tex]\( 50 - 10 = 40 \)[/tex]
- Scale 4: [tex]\( 40 - 25 = 15 \)[/tex]
5. Choose the scale with the maximum difference between its endpoints:
- The scale with the maximum difference is Scale 1, with a value of 50.
6. Conclusion:
- The best scale for the vertical axis that maximizes the difference in the heights of the bars is the 0-50 scale.
Therefore, Gemma should use the scale 0-50 for the vertical axis of her histogram.
