Analyzing and Graphing Data
Imagine you run a lemonade stand at the school science fair and want to know if more sugar makes people like the drink more. You collect 30 ratings. A pile of numbers doesn't tell you anything yet. Data analysis turns the pile into an answer, and also tells you how much to trust that answer. By the end of this page, you will be able to say exactly how much trust your own data deserves.
Measuring in SI and organizing data
Scientists everywhere use the same measuring system, the International System of Units (SI), so that anyone can repeat an experiment and compare results. In a biology lab you will mostly use these:
| Quantity | SI unit used in lab | Tool |
|---|---|---|
| Mass | gram (g), kilogram (kg) | digital balance |
| Length | meter (m), centimeter (cm), millimeter (mm) | metric ruler |
| Volume of a liquid | liter (L), milliliter (mL) | graduated cylinder, pipet |
| Temperature | degrees Celsius (°C) | thermometer, probe |
| Time | second (s), minute (min) | stopwatch |
Data comes in two kinds. Quantitative data are numbers with units (a seed with a mass of 0.42 g). Qualitative data are descriptions (the leaf is dark green and curled).
Put your measurements in a data table. Give it a title, put the units in the column headings (not in every cell), and make each row one trial or one condition.
Every experiment also has three kinds of variables:
Which SI unit would a scientist use to measure each of the following: (a) the mass of a seed, (b) the length of a leaf, (c) the volume of a liquid in a graduated…
Which SI unit would a scientist use to measure each of the following: (a) the mass of a seed, (b) the length of a leaf, (c) the volume of a liquid in a graduated cylinder, (d) the temperature of a water bath?
Calculating a mean
Real measurements vary a little. A balance might read 0.42 g one time and 0.45 g for another seed. To summarize several values with one number, scientists use the mean (the average).
The mean works like leveling out: if every value were shared equally, each would equal the mean.
The range (largest value minus smallest value) tells you how spread out the data are. Two groups can have similar means but very different ranges, and that matters, as you will see below.
Emma recorded the mass of five seeds in grams: 0.42, 0.45, 0.40, 0.47, 0.41. Calculate the mean (average) mass of the seeds. Write your answer with the correct unit.
Emma recorded the mass of five seeds in grams: 0.42, 0.45, 0.40, 0.47, 0.41. Calculate the mean (average) mass of the seeds. Write your answer with the correct unit.
Jayden measures the time for a tablet to dissolve in water at different temperatures. He runs each temperature three times. | Water temperature (°C) | Trial 1 (s) |…
Jayden measures the time for a tablet to dissolve in water at different temperatures. He runs each temperature three times.
| Water temperature (°C) | Trial 1 (s) | Trial 2 (s) | Trial 3 (s) |
|---|---|---|---|
| 10 | 90 | 96 | 84 |
| 30 | 52 | 50 | 54 |
| 50 | 28 | 30 | 26 |
- a) Calculate the mean dissolving time at each temperature.
- b) Describe the relationship between temperature and dissolving time.
- c) Explain why running three trials is better than running one.
Choosing and drawing graphs
A graph lets you see a pattern at a glance. Which graph you pick depends on your data.
| Graph | Use it when… | Example |
|---|---|---|
| Bar graph | the independent variable is a category | average height of plants with Fertilizer X, Y, or none |
| Line graph | the independent variable is continuous (time, temperature, distance) and you want to show a trend | height of a bean plant every 2 days |
| Scatter plot | you want to see whether two measured variables are related | foot length vs. height of students |
Rules for any graph:
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The independent variable goes on the x-axis (horizontal). The dependent variable goes on the y-axis (vertical).
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Label each axis with the variable and its unit, for example "Time (days)".
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Use an even scale and a descriptive title.
To describe a trend, use words like increases, decreases, levels off, or peaks and then drops. Add numbers from the graph: "The bubble rate fell from 48 to 10 bubbles per minute."
A student measures the height of a bean plant every 2 days. State which type of graph (bar graph or line graph) is best for showing how the height changes over time, and…
A student measures the height of a bean plant every 2 days. State which type of graph (bar graph or line graph) is best for showing how the height changes over time, and explain why. Then say which variable goes on the x-axis and which on the y-axis.
The table shows the number of bubbles of oxygen produced per minute by an aquatic plant at different distances from a lamp. | Distance from lamp (cm) | Bubbles per…
The table shows the number of bubbles of oxygen produced per minute by an aquatic plant at different distances from a lamp.
| Distance from lamp (cm) | Bubbles per minute |
|---|---|
| 10 | 48 |
| 20 | 30 |
| 30 | 18 |
| 40 | 10 |
- a) Describe the pattern in the data.
- b) Identify the independent and dependent variables.
- c) Calculate how much the bubble rate decreased from 10 cm to 40 cm, as a percent of the rate at 10 cm. Round to the nearest whole percent.
Reading patterns without overreaching
Data do not always go up or down forever. In many biology experiments, there is an optimum, a best value, and results fall off on both sides. Enzymes, seed germination, and brine shrimp hatching all behave this way.
Look at this sketch of hatching vs. salt concentration (the shape matches the kind of data in the practice problems):
A conclusion must stay inside the range you tested. If hatching rose from 0 to 30 g/L and then fell at 40 and 50 g/L, you cannot say "more salt always helps." You can say "hatching was highest near 30 g/L in this experiment."
A good conclusion uses CER:
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Claim: a one-sentence answer to the question.
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Evidence: specific data (numbers, means, ranges).
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Reasoning: the scientific idea that links the evidence to the claim.
A class tests how the concentration of salt in water affects the percent of brine shrimp eggs that hatch. Each group used 100 eggs per container. | Salt concentration…
A class tests how the concentration of salt in water affects the percent of brine shrimp eggs that hatch. Each group used 100 eggs per container.
| Salt concentration (g/L) | Eggs hatched (of 100) |
|---|---|
| 0 | 4 |
| 10 | 38 |
| 20 | 72 |
| 30 | 85 |
| 40 | 61 |
| 50 | 12 |
- a) Describe the relationship between salt concentration and hatching, including the approximate concentration that appears best.
- b) Calculate the rate of change in hatching (eggs per g/L) between 10 and 20 g/L and between 40 and 50 g/L.
- c) Explain why a conclusion that "more salt always increases hatching" is not supported.
- d) Identify two limitations of the data and propose one improvement.
Marcus compares two fertilizers. He measures plant height (cm) after 21 days in five plants for each group. | Group | Plant 1 | Plant 2 | Plant 3 | Plant 4 | Plant 5 |…
Marcus compares two fertilizers. He measures plant height (cm) after 21 days in five plants for each group.
| Group | Plant 1 | Plant 2 | Plant 3 | Plant 4 | Plant 5 |
|---|---|---|---|---|---|
| Control (water only) | 14 | 15 | 13 | 16 | 12 |
| Fertilizer X | 19 | 21 | 20 | 18 | 22 |
| Fertilizer Y | 15 | 28 | 12 | 24 | 11 |
- a) Calculate the mean height for each group and the range for each group.
- b) Marcus says Fertilizer Y is just as good as Fertilizer X because the means are similar. Use the means and ranges to evaluate his claim.
- c) Write a claim-evidence-reasoning (CER) statement about which treatment most reliably increased growth.
Sources of error and limits of data
No experiment is perfect. A source of error is anything that makes your measurements differ from the true value or from each other. Knowing the likely errors helps you decide how much to trust the data.
| Type | What it is | Example | How to reduce it |
|---|---|---|---|
| Random error | unpredictable ups and downs | reading a ruler slightly differently each time | repeat trials and take the mean |
| Systematic error | the same push in one direction every time | a balance that is not zeroed, so all masses read 0.5 g too high | calibrate tools, use the same tool throughout |
| Human error | mistakes in technique | miscounting cells, starting the stopwatch late | careful procedure, have two people check |
Other ways to improve data:
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Repeat trials. More trials make the mean more trustworthy, and one odd result stands out.
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Larger sample size. Ten plants tell you more than two.
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Use the same equipment for all measurements so differences come from the independent variable, not the tool.
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Include a control group to compare against.
Olivia counts the number of yeast cells in a sample every hour. A line graph of her data shows that the number of cells stays about the same for the first 2 hours, then…
Olivia counts the number of yeast cells in a sample every hour. A line graph of her data shows that the number of cells stays about the same for the first 2 hours, then rises steeply from hour 2 to hour 6, and then levels off. Her lab partner points out that the hour 4 measurement was taken with a different microscope.
- a) Suggest one reason the population might level off after hour 6.
- b) Identify a possible source of error in her data and explain how it could affect the results.
- c) Describe one way to reduce that error.
Summary
Back to the lemonade stand: collect the ratings in a table, find the mean for each sugar level, graph sugar (independent, x-axis) against rating (dependent, y-axis), and then write a CER statement. Check the range and the likely sources of error before deciding how far to trust your result.
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Use SI units (g, cm, mL, °C, s) and organize data in titled tables with units in the headings.
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The independent variable is changed; the dependent variable is measured; controlled variables stay the same.
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Mean = sum $\div$ number of values. The range shows how spread out the data are.
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Bar graph for categories, line graph for trends over a continuous variable, scatter plot for relationships. Independent variable on x, dependent on y, axes labeled with units.
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Conclusions stay within the tested range and use claim, evidence, reasoning.
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Sources of error (random, systematic, human) limit data. Repeat trials, use more samples, and calibrate tools to reduce them.