Lesson 1.4 · Unit 1 · NGSS practice 4
Reading biological data, and the graph that misleads
A graph is an argument in a picture, and like any argument it can be made honestly or dishonestly with the same true numbers. The skill this lesson builds is boring and valuable: describe what the data do before you explain why, and check the axes before you believe the shape.
- Describe before you explain. First say what the values do (rise, fall, peak, level off, and by how much). Only then say why. Students who explain first usually describe a trend the data do not show.
- Match the graph type to the data. A line graph needs a continuous independent variable such as time or distance. Separate categories take a bar chart, and joining category bars with a line implies values in between that do not exist.
- The independent variable goes on the horizontal axis, the dependent on the vertical, both labeled with units.
- A truncated vertical axis exaggerates. Starting the scale at 95 rather than 0 can turn a two percent difference into a picture of a cliff. Always read where the axis begins.
- Quote figures when you describe. "Oxygen fell from 8.2 to 2.4 milligrams per liter over the first two kilometers" is a description. "Oxygen went down" is not.
- A trend is not a mechanism. The graph shows what happened; the explanation comes from biology you bring to it.
Where students lose marks: writing "the graph increases". The graph does not increase; the measured quantity does. Name the variable, give the direction, and quote the numbers with units.
The data. Dissolved oxygen measured downstream of a sewage outfall. The figures are constructed so the pattern is clear.
| Distance downstream (km) | 0 | 1 | 2 | 4 | 8 | 16 |
|---|---|---|---|---|---|---|
| Dissolved oxygen (mg/L) | 8.2 | 3.1 | 2.4 | 4.0 | 6.5 | 8.0 |
Step one: choose the graph type. Distance is continuous, so a line graph is right. Distance goes on the horizontal axis, dissolved oxygen on the vertical, both with units.
Step two: describe the overall shape. Oxygen falls steeply, reaches a minimum, then recovers. The curve is a sag, and naming the shape before the numbers helps organize the description.
Step three: quantify the fall. From 8.2 mg/L at the outfall to 2.4 mg/L at 2 km: a drop of 5.8 mg/L, which is about 71 percent of the starting value, across only two kilometers.
Step four: locate the minimum and the recovery. The lowest value, 2.4 mg/L, occurs at 2 km. By 16 km oxygen has returned to 8.0 mg/L, close to the 8.2 mg/L measured at the outfall itself.
Step five: note that the recovery is slower than the fall. Oxygen loses 5.8 mg/L in 2 km but needs 14 km to regain 5.6 mg/L. Describing the asymmetry is the part most students miss.
Step six: now explain. Organic matter in sewage feeds bacteria, whose aerobic respiration consumes dissolved oxygen faster than the river can absorb it from the air. As the organic matter is used up downstream, bacterial numbers fall, consumption drops below the rate of reaeration, and oxygen climbs back. Every part of this explanation comes from biology, not from the graph.
Step seven: check how the axis could mislead. Plotted from 0 to 10 mg/L the sag is dramatic and honest. Plotted from 2 to 9 mg/L it would look catastrophic; plotted from 0 to 100 it would look like nothing happened. The numbers are identical in all three.
Questions 1 to 5 are recall. Questions 6 to 10 ask for reasoning.
- Which axis carries the independent variable?
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The horizontal axis
- When is a bar chart correct rather than a line graph?
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When the independent variable is separate categories rather than a continuous quantity
- In the worked example, what is the minimum oxygen value and where does it occur?
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2.4 mg/L at 2 km downstream
- By how much does oxygen fall between 0 and 2 km?
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From 8.2 to 2.4 mg/L, a fall of 5.8 mg/L
- What is wrong with the sentence "the graph increases"?
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The graph does not increase; the measured quantity does, and it must be named with units
- Explain how starting a vertical axis at 95 rather than 0 can mislead, without
any number being false.
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Every plotted value can be perfectly accurate while the picture is misleading, because the eye judges the size of a difference from the height of the bars or the steepness of the line rather than from the numbers. If two values are 96 and 98 and the axis runs from 95 to 100, the second bar appears three times the height of the first, suggesting a large effect where the real difference is about two percent. Nothing is fabricated; the scale has simply been chosen to magnify. The eye reads relative heights, which a truncated scale exaggerates
- Why is describing the trend before explaining it worth the extra sentence?
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Because an explanation offered first tends to determine what you think you see. A student who begins with "bacteria used up the oxygen" will often describe a steady decline and miss the recovery entirely, since the explanation they reached for does not include one. Describing first forces the actual shape into view, including the parts that need accounting for, and it is also how these questions are marked: the description and the explanation earn separate credit. Explaining first makes you describe the data you expected rather than the data present
- The recovery takes far longer than the fall. Suggest a biological reason.
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The fall is driven by bacterial respiration, which is fast because the sewage supplies a large concentrated pulse of organic matter and bacterial populations can grow rapidly. The recovery depends on oxygen dissolving back into the water from the atmosphere, which happens only at the surface and at a rate set by turbulence and surface area rather than by biology. A fast biological process removes the oxygen and a slow physical process replaces it, so the curve is steep going down and gradual coming back. Fast bacterial consumption against slow physical reaeration
- A student joins the tops of four bars showing mean masses of four different
species with a line. Explain why this is wrong.
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A line asserts that values exist between the plotted points, so joining the bars claims there are organisms partway between two species with intermediate masses. Species are separate categories, not points on a continuous scale, and the order of the bars is arbitrary, so the line's slope carries no meaning and would change if the bars were rearranged. A bar chart keeps the categories distinct, which is the honest representation of this kind of data. A line implies intermediate values, and species are discrete categories
- What could you not conclude from this graph alone, even though the pattern is
clear?
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You could not conclude that the sewage outfall caused the oxygen sag, because nothing was changed on purpose and no comparison river was measured. The pattern is consistent with that explanation, but an unmeasured factor changing along the same stretch, such as a change in depth, flow rate or temperature, could also lower oxygen. Supporting the causal claim would need either upstream measurements, a comparable river without an outfall, or records from before the outfall existed. That the outfall caused the sag, since nothing was controlled or compared