Question

gemma is creating a histogram based on the table below.
salary range | number of people
0 - $19,999 | 40
$20,000 - $39,999 | 30
$40,000 - $59,999 | 35
which scale can she use for the vertical axis such that the difference in the heights of the bars is maximized?
0–50
0–40
10–50
25–40

Explanation:

Step1: Analyze the data values

The number of people for each salary range are 40, 30, and 35. The minimum value is 30 and the maximum is 40.

Step2: Evaluate each scale

• Scale 0 - 50: The range is large, so the difference in bar heights might be less noticeable.
• Scale 0 - 40: The maximum value (40) is at the top, but the minimum (30) is also within this range. However, let's check other scales.
• Scale 10 - 50: The minimum value is 30, so starting at 10, but the range from 10 to 50 is still broad.
• Scale 25 - 40: The minimum value among the number of people is 30, and the maximum is 40. This scale is from 25 to 40, so it includes all the data points (30, 35, 40) and has a smaller range compared to others. A smaller vertical scale range (when the data fits) will make the differences in bar heights more pronounced (maximize the difference in heights) because the same difference in the number of people will correspond to a larger fraction of the scale's height. For example, if the scale is 25 - 40 (a range of 15), a difference of 5 (e.g., 40 - 35) is $\frac{5}{15}=\frac{1}{3}$ of the scale, whereas in a scale like 0 - 50 (range 50), the same difference is $\frac{5}{50}=\frac{1}{10}$ of the scale. So the smaller the scale range (that still contains all data), the more the bar height differences are maximized. The data points are 30, 35, 40. The scale 25 - 40 includes all of them (25 ≤ 30, 35, 40 ≤ 40). The other scales either start too low (0 - 50, 0 - 40, 10 - 50) which makes the range larger, thus reducing the relative difference in bar heights.

Answer:

25–40