Question

what incorrect conclusions could be drawn from the graph given in the example? select all that apply.
growth chart of a child
160 cm
140 cm
130
120 cm
120
110
100 cm
100
90
80 cm
75
2
4
5
9
10
ages (in years)
select all that apply:
height may be mistaken for weight.
the relative change in height over the age range could seem smaller than it really is.
the relationship between height and age over the given age range may be assumed to be approximately linear when it is not
the tick-marks on the x-axis are evenly spaced, making the ages evenly scaled.

Explanation:

1. Analyze "Height may be mistaken for weight": The graph's y - axis is labeled height, so this is not a likely incorrect conclusion.
2. Analyze "The relative change in height over the age range could seem smaller than it really is": The y - axis starts at 75 cm (not 0), which can compress the visual perception of the relative change, making it seem smaller than it actually is.
3. Analyze "The relationship between height and age over the given age range may be assumed to be approximately linear when it is not": The graph shows a straight - line plot, but we don't know the actual underlying relationship. However, the main issue with the graph's axis scaling (x - axis tick - marks are not evenly spaced in terms of age intervals: from 2 to 4 is 2 years, 4 to 5 is 1 year, 5 to 9 is 4 years, 9 to 10 is 1 year) is more about the x - axis scaling. The linear appearance here is not the main incorrect conclusion from the graph's axis design.
4. Analyze "The tick - marks on the x - axis are evenly spaced, making the ages evenly scaled": The x - axis has tick - marks at 2, 4, 5, 9, 10. The intervals between them (2 - 4: 2 years, 4 - 5: 1 year, 5 - 9: 4 years, 9 - 10: 1 year) are not equal, but the tick - marks are evenly spaced visually. This can lead to the incorrect conclusion that the ages are evenly scaled (i.e., the time intervals between the ages are the same), which is not true. Also, as mentioned before, the y - axis starting at 75 cm can make the relative change in height seem smaller.

So the incorrect conclusions are "The relative change in height over the age range could seem smaller than it really is" and "The tick - marks on the x - axis are evenly spaced, making the ages evenly scaled".

Answer:

• The relative change in height over the age range could seem smaller than it really is.
• The tick - marks on the \( x \) - axis are evenly spaced, making the ages evenly scaled.