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 is labeled for height, but without context, someone might confuse the vertical axis (height) with weight, but this is less about the graph's design error for incorrect conclusions here.
2. Analyze "The relative change in height over the age range could seem smaller than it really is": The y - axis starts at 75 (not 0), which can compress the visual perception of height change, making relative change seem smaller.
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 plotted points lie close to a straight line, so this is not an incorrect conclusion drawn from the graph (the relationship here looks linear).
4. Analyze "The tick - marks on the \(x\) - axis are evenly spaced, making the ages evenly scaled": The \(x\) - axis has ticks at 2, 4, 5, 9, 10. The intervals between 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), which can mislead people into thinking the age scale is even. Also, the y - axis starting at 75 (not 0) affects the perception of relative change. So the incorrect conclusions come from the second and fourth options (and also, the first option is less relevant, but the key ones are about the axis scaling). Wait, re - evaluating:

• For "The tick - marks on the \(x\) - axis are evenly spaced, making the ages evenly scaled": The \(x\) - axis ticks are spaced evenly (same distance between marks), but the age intervals between them (2 - 4: 2 years, 4 - 5: 1 year, 5 - 9: 4 years, 9 - 10: 1 year) are not equal. So people might incorrectly think the age scale is even (linear in terms of age intervals) because of the even tick spacing.
• For "The relative change in height over the age range could seem smaller than it really is": When a graph's y - axis does not start at 0, the visual representation of change is compressed. For example, if the y - axis started at 0, the increase from 75 to 130 would look more significant. Since it starts at 75, the "rise" in the graph looks less steep, so the relative change seems smaller.
• The first option: The graph is clearly labeled for height, so mistaking height for weight is not a conclusion drawn from the graph's design (it's about misinterpreting the variable, not the graph's visual cues for incorrect conclusions about the relationship or scale).
• The third option: The points lie close to a straight line, so assuming linearity is a correct observation from the graph.

So the incorrect conclusions are from "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.