Reading Data, Graphs & Drawing Conclusions
Learn how to pick the right graph for your data, describe an overall trend, and write conclusions that answer the question — plus why correlation isn't causation.
What you'll do in this lesson
A voice-first session with the Crimsora tutor on Reading Data, Graphs & Drawing Conclusions, then targeted practice and FRQs — with the tutor adapting to where you get stuck.
What this lesson covers
You ran the investigation, you filled the data table, and now you are staring at a page of numbers. What do those numbers actually say? This lesson is about the last two steps of any experiment: turning data into a picture, and turning that picture into an honest statement about the world.
Three skills matter here. First, choosing a graph that fits the kind of data you collected — a bar graph and a line graph are not interchangeable. Second, describing the overall pattern instead of pointing at one interesting dot. Third, writing a conclusion that states what your evidence shows, answers the question you started with, and admits what the evidence does not show. That last part includes one of the most important rules in all of science: two things changing together does not prove that one caused the other.
Three skills matter here. First, choosing a graph that fits the kind of data you collected — a bar graph and a line graph are not interchangeable. Second, describing the overall pattern instead of pointing at one interesting dot. Third, writing a conclusion that states what your evidence shows, answers the question you started with, and admits what the evidence does not show. That last part includes one of the most important rules in all of science: two things changing together does not prove that one caused the other.
Choosing a Graph That Fits Your Data
The graph you choose depends on what kind of variable you put on the horizontal axis. If the independent variable is made of separate categories — brands of paper towel, types of soil, students' favorite habitat — you have categorical data and you need a bar graph. If the independent variable is a number that could take any value in between — time, temperature, mass, distance — you have continuous data and a line graph is usually right, because the line between two points means something.
Always put the independent variable (what you changed) on the x-axis and the dependent variable (what you measured) on the y-axis. Label both axes with the quantity and the unit, choose a scale with even intervals, and give the graph a title that names both variables.
Where students go wrong: drawing a line graph for categorical data. If your x-axis reads "sand, clay, potting soil," connecting the bars with a line claims there is something halfway between sand and clay. There isn't. Another frequent error is a scale with uneven jumps — 0, 5, 10, 50, 100 — which stretches part of the graph and makes a small change look enormous.
| Graph type | Use it when | Example |
|---|---|---|
| Bar graph | Comparing separate categories | Plant growth in sand, clay, and potting soil |
| Line graph | Showing how something changes across a continuous variable | Water temperature every 2 minutes for 20 minutes |
| Scatter plot | Looking for a relationship between two measured numbers | Arm span vs. height for 30 students |
| Pie chart | Showing parts of one whole (percentages) | What fraction of the class chose each answer |
Where students go wrong: drawing a line graph for categorical data. If your x-axis reads "sand, clay, potting soil," connecting the bars with a line claims there is something halfway between sand and clay. There isn't. Another frequent error is a scale with uneven jumps — 0, 5, 10, 50, 100 — which stretches part of the graph and makes a small change look enormous.
Describing the Trend, Not One Point
A trend is the overall pattern in the data — the direction the numbers move as the independent variable increases. When your teacher asks you to describe the data, they want the shape of the whole graph, not a tour of individual points.
Useful trend language: increases, decreases, stays roughly constant, increases then levels off, increases quickly at first then slowly, peaks at a certain value then falls. Then add numbers to make it specific. "As fertilizer increased from 0 to 6 grams, average plant height increased from 8 cm to 21 cm, but from 6 to 10 grams the height stayed near 21 cm." That sentence names the direction, gives the range, and points out where the pattern changes.
An outlier is a single data point that sits far away from the pattern. Mention it, but do not let it hijack your description. Say "one trial at 4 grams gave 30 cm, well above the other trials at that amount," then continue describing the trend. An outlier may come from a measurement mistake, a plant that was already taller, or real variation — you cannot tell which without more information, so do not silently delete it.
The most common mistake in this lesson is writing a conclusion built on one point: "Fertilizer works because the tallest plant got 6 grams." One tall plant is not a pattern. It could be that plant's genetics, its spot near the window, or a lucky measurement. A trend is convincing because it repeats across many points, and repeated trials at each level make the trend trustworthy.
Useful trend language: increases, decreases, stays roughly constant, increases then levels off, increases quickly at first then slowly, peaks at a certain value then falls. Then add numbers to make it specific. "As fertilizer increased from 0 to 6 grams, average plant height increased from 8 cm to 21 cm, but from 6 to 10 grams the height stayed near 21 cm." That sentence names the direction, gives the range, and points out where the pattern changes.
An outlier is a single data point that sits far away from the pattern. Mention it, but do not let it hijack your description. Say "one trial at 4 grams gave 30 cm, well above the other trials at that amount," then continue describing the trend. An outlier may come from a measurement mistake, a plant that was already taller, or real variation — you cannot tell which without more information, so do not silently delete it.
The most common mistake in this lesson is writing a conclusion built on one point: "Fertilizer works because the tallest plant got 6 grams." One tall plant is not a pattern. It could be that plant's genetics, its spot near the window, or a lucky measurement. A trend is convincing because it repeats across many points, and repeated trials at each level make the trend trustworthy.
Writing a Conclusion With Three Parts
A complete conclusion does three jobs, and students who skip one of them usually skip the third.
First, state what the evidence shows. Quote actual numbers from your data — the starting value, the ending value, the size of the difference. "Cups with lids lost an average of 4 degrees Celsius in 15 minutes; cups without lids lost an average of 11 degrees Celsius."
Second, answer the original question. Go back and reread the question you wrote at the start of the investigation. If the question was "Does a lid slow down heat loss from hot water?" then your conclusion must contain a yes-or-no style answer: "Yes — in this test, lids slowed cooling." A pile of numbers with no answer leaves the reader to guess what you concluded.
Third, say what the evidence does not show. Every investigation has limits. Maybe you only tested one cup size, ran three trials, measured for 15 minutes, or used one brand of lid. Write those limits down: "This test does not show whether lids help over a full hour, or whether the same thing happens with cold drinks." Naming limits is not admitting failure — it is what makes a claim scientific rather than an opinion.
A useful frame is claim, evidence, reasoning. The claim answers the question. The evidence is the specific data. The reasoning explains how the evidence supports the claim, usually by connecting it to science you already know: a lid blocks warm air and water vapor from escaping, so less energy leaves the cup.
Avoid words like "proves" and "always." Science supports and gives evidence for claims; it rarely proves them for all situations.
First, state what the evidence shows. Quote actual numbers from your data — the starting value, the ending value, the size of the difference. "Cups with lids lost an average of 4 degrees Celsius in 15 minutes; cups without lids lost an average of 11 degrees Celsius."
Second, answer the original question. Go back and reread the question you wrote at the start of the investigation. If the question was "Does a lid slow down heat loss from hot water?" then your conclusion must contain a yes-or-no style answer: "Yes — in this test, lids slowed cooling." A pile of numbers with no answer leaves the reader to guess what you concluded.
Third, say what the evidence does not show. Every investigation has limits. Maybe you only tested one cup size, ran three trials, measured for 15 minutes, or used one brand of lid. Write those limits down: "This test does not show whether lids help over a full hour, or whether the same thing happens with cold drinks." Naming limits is not admitting failure — it is what makes a claim scientific rather than an opinion.
A useful frame is claim, evidence, reasoning. The claim answers the question. The evidence is the specific data. The reasoning explains how the evidence supports the claim, usually by connecting it to science you already know: a lid blocks warm air and water vapor from escaping, so less energy leaves the cup.
Avoid words like "proves" and "always." Science supports and gives evidence for claims; it rarely proves them for all situations.
Two Things Changing Together Is Not Proof of Cause
Correlation means two measurements change together in a predictable way. Causation means one of them actually makes the other happen. Correlation is easy to see on a scatter plot. Causation requires a controlled experiment.
Here is a classic example. Across the months of a year, ice cream sales and swimming pool injuries rise and fall together. Nobody thinks ice cream causes injuries. A third factor — hot summer weather — causes both. That hidden third factor is called a confounding variable, and it is the number one reason a correlation can fool you.
There are three explanations whenever you see two variables moving together. One, A causes B. Two, B causes A (the direction could be backwards — do heavier backpacks cause back pain, or do students with back pain pack differently?). Three, something else causes both. Coincidence in a small sample is a fourth possibility.
What lets you argue for causation? A controlled investigation, the kind you planned earlier in this unit, where you change one variable on purpose, hold the others constant, and compare against a control group. Observational data — surveys, records, measurements you did not control — can reveal a correlation worth investigating, but it cannot settle the cause by itself.
So when data are observational, write your conclusion carefully: "Students who ate breakfast had higher average quiz scores, but this survey does not show that breakfast caused the difference. Students who eat breakfast may also sleep more or have different study habits." That sentence reports the pattern honestly and refuses to overclaim — exactly what scientists reading your work are looking for.
Here is a classic example. Across the months of a year, ice cream sales and swimming pool injuries rise and fall together. Nobody thinks ice cream causes injuries. A third factor — hot summer weather — causes both. That hidden third factor is called a confounding variable, and it is the number one reason a correlation can fool you.
There are three explanations whenever you see two variables moving together. One, A causes B. Two, B causes A (the direction could be backwards — do heavier backpacks cause back pain, or do students with back pain pack differently?). Three, something else causes both. Coincidence in a small sample is a fourth possibility.
What lets you argue for causation? A controlled investigation, the kind you planned earlier in this unit, where you change one variable on purpose, hold the others constant, and compare against a control group. Observational data — surveys, records, measurements you did not control — can reveal a correlation worth investigating, but it cannot settle the cause by itself.
So when data are observational, write your conclusion carefully: "Students who ate breakfast had higher average quiz scores, but this survey does not show that breakfast caused the difference. Students who eat breakfast may also sleep more or have different study habits." That sentence reports the pattern honestly and refuses to overclaim — exactly what scientists reading your work are looking for.
Reading Graphs Other People Made
You will read far more graphs than you draw, and a graph can mislead without containing a single false number. Before you trust one, run through a quick inspection.
Check the axis labels and units first. A y-axis reading "mass (g)" tells a very different story from "mass (kg)." Next, check where the y-axis starts. A bar graph whose axis begins at 90 instead of 0 turns a change from 92 to 96 into a bar that looks twice as tall. The data are honest; the picture is not.
Check the scale intervals. Even spacing between numbers is required for the shape of the line to mean anything. Then check the sample size and whether the values are averages of repeated trials. A line built from single measurements can wander for reasons that have nothing to do with your variable.
Finally, ask what is missing. Does the graph show a control group? Over what range was the variable tested? A graph showing plant growth from 0 to 10 grams of fertilizer says nothing about 50 grams — extending a trend past your data is called extrapolation, and it is a guess, not a finding.
To read a specific value, find the number on the x-axis, move straight up to the line or bar, then straight across to the y-axis. To find the biggest change, look for the steepest part of a line, not the highest point. Highest and fastest-changing are different questions, and mixing them up is one of the most common errors students make when interpreting line graphs.
Check the axis labels and units first. A y-axis reading "mass (g)" tells a very different story from "mass (kg)." Next, check where the y-axis starts. A bar graph whose axis begins at 90 instead of 0 turns a change from 92 to 96 into a bar that looks twice as tall. The data are honest; the picture is not.
Check the scale intervals. Even spacing between numbers is required for the shape of the line to mean anything. Then check the sample size and whether the values are averages of repeated trials. A line built from single measurements can wander for reasons that have nothing to do with your variable.
Finally, ask what is missing. Does the graph show a control group? Over what range was the variable tested? A graph showing plant growth from 0 to 10 grams of fertilizer says nothing about 50 grams — extending a trend past your data is called extrapolation, and it is a guess, not a finding.
To read a specific value, find the number on the x-axis, move straight up to the line or bar, then straight across to the y-axis. To find the biggest change, look for the steepest part of a line, not the highest point. Highest and fastest-changing are different questions, and mixing them up is one of the most common errors students make when interpreting line graphs.
Key terms
- Trend.
- The overall pattern or direction in a data set as the independent variable changes — increasing, decreasing, leveling off, or peaking — rather than the value of any single point.
- Categorical data.
- Data sorted into separate, non-numerical groups such as soil types or brands. Best displayed with a bar graph, since there are no values in between the categories.
- Continuous data.
- Numerical data that can take any value within a range, such as time, temperature, or mass. Best displayed with a line graph or scatter plot.
- Outlier.
- A data point that lies far from the overall pattern. It should be reported and considered, not quietly removed, because it may signal a measurement error or real variation.
- Correlation.
- A relationship in which two measured variables change together in a predictable way. Correlation shows a pattern exists but does not identify what causes it.
- Causation.
- A relationship in which changing one variable actually produces the change in the other. Supported by controlled experiments, not by observational data alone.
- Confounding variable.
- A third factor that affects both variables being compared, creating a correlation between them even when neither one causes the other.
- Extrapolation.
- Extending a trend beyond the range of values actually tested. It produces a prediction, not evidence, because the pattern may change outside the tested range.
Worked example
Mia investigated the question "Does the amount of salt dissolved in water affect how long it takes the water to freeze?" She used identical cups with 100 mL of water each, added different masses of salt, placed all cups in the same freezer, and recorded the freezing time. She ran three trials at each salt level and averaged them.
Choose a graph, describe the trend, and write a complete conclusion.
| Salt added (g) | Average freezing time (min) |
|---|---|
| 0 | 42 |
| 2 | 56 |
| 4 | 71 |
| 6 | 88 |
| 8 | 104 |
Step 1: Choose the graph. The independent variable is salt added in grams — a continuous number, since 3 g or 5.5 g would also be possible. Continuous independent variable means a line graph. Salt added goes on the x-axis (0 to 8 g), average freezing time on the y-axis (0 to about 110 min). Title: "Effect of Dissolved Salt on Freezing Time of 100 mL of Water."
Step 2: Describe the trend. As salt increased from 0 g to 8 g, average freezing time increased steadily from 42 minutes to 104 minutes. Check whether the increase is steady by finding the change per step: from 0 to 2 g the time rose 14 min, then 15 min, then 17 min, then 16 min. Those jumps are close to equal, so the trend is close to a straight line. The total change is minutes, and the freezing time at 8 g is about 2.5 times the time with no salt.
Step 3: Answer the original question. Yes — in this investigation, adding salt increased the time it took the water to freeze.
Step 4: Give the reasoning. Salt dissolved in water lowers its freezing point, so the water must reach a colder temperature before ice forms, which takes longer in a freezer held at a fixed temperature.
Step 5: State what the evidence does not show. This test used only 100 mL of water, one freezer, one type of salt, and salt amounts from 0 to 8 g. It does not show what happens above 8 g, whether the pattern stays straight at higher amounts, or whether sugar would do the same thing. Because Mia controlled the other variables and used a control cup with 0 g of salt, she can reasonably claim that salt caused the change — this is an experiment, not just an observed correlation.
Step 2: Describe the trend. As salt increased from 0 g to 8 g, average freezing time increased steadily from 42 minutes to 104 minutes. Check whether the increase is steady by finding the change per step: from 0 to 2 g the time rose 14 min, then 15 min, then 17 min, then 16 min. Those jumps are close to equal, so the trend is close to a straight line. The total change is minutes, and the freezing time at 8 g is about 2.5 times the time with no salt.
Step 3: Answer the original question. Yes — in this investigation, adding salt increased the time it took the water to freeze.
Step 4: Give the reasoning. Salt dissolved in water lowers its freezing point, so the water must reach a colder temperature before ice forms, which takes longer in a freezer held at a fixed temperature.
Step 5: State what the evidence does not show. This test used only 100 mL of water, one freezer, one type of salt, and salt amounts from 0 to 8 g. It does not show what happens above 8 g, whether the pattern stays straight at higher amounts, or whether sugar would do the same thing. Because Mia controlled the other variables and used a control cup with 0 g of salt, she can reasonably claim that salt caused the change — this is an experiment, not just an observed correlation.
Practice questions
A student surveys 200 middle schoolers and finds that students who own more pairs of shoes tend to read at a higher grade level. Which conclusion is best supported by this data?
- Owning more shoes improves a student's reading ability.
- Reading more books causes students to buy more shoes.
- There is a correlation between shoe ownership and reading level, but this survey does not show what causes it.
- There is no relationship between the two variables.
Answer: There is a correlation between shoe ownership and reading level, but this survey does not show what causes it.
The survey is observational — the student did not change anything or control other variables — so it can only reveal that two things change together. A confounding variable such as family income or access to books and tutoring could easily affect both. Saying there is no relationship contradicts the data, and both cause-and-effect statements claim more than a survey can support. Only a controlled investigation could test whether one variable actually produces the other.
Which graph type best fits data comparing the average number of dandelions per square meter in four different school lawns: the soccer field, the courtyard, the front lawn, and the shaded area behind the gym?
- Line graph
- Bar graph
- Pie chart
- Scatter plot
Answer: Bar graph
The independent variable is location, which is categorical — four separate places with nothing in between them. A bar graph compares separate categories directly. A line graph would wrongly imply values exist between the courtyard and the front lawn. A pie chart shows parts of one whole, but these are separate density measurements, not slices of a single total. A scatter plot needs two measured numerical variables.
A class measured how far a toy car rolled after being released from ramps of different heights. Distance increased steadily from a ramp height of 10 cm to 40 cm, then barely changed from 40 cm to 60 cm. One trial at 30 cm gave a distance far shorter than the others at that height. Write a description of the trend and a conclusion that includes what the evidence does not show.
Answer: Trend: As ramp height increased from 10 cm to 40 cm, rolling distance increased steadily; from 40 cm to 60 cm the distance leveled off and stayed nearly constant. One trial at 30 cm was an outlier, much shorter than the other trials at that height, possibly because the car was released unevenly or hit an obstacle. Conclusion: Yes, ramp height affects rolling distance — greater height gave greater distance up to about 40 cm, after which extra height produced almost no additional distance. This is likely because a higher release point gives the car more energy of motion at the bottom, until friction and air resistance limit how far it can travel. What the evidence does not show: it does not show what happens above 60 cm, whether a different car or floor surface would produce the same leveling-off point, or exactly why the 30 cm outlier occurred.
A complete answer names the direction of change with numbers, identifies where the pattern changes rather than describing every point, mentions the outlier without letting it drive the conclusion, answers the original question directly, gives reasoning, and states the limits of the investigation. Answers that stop after "the higher the ramp, the farther it went" miss the leveling-off, which is the most interesting feature of the data.
FAQ
- How do I know whether to use a bar graph or a line graph?
- Look at your independent variable, the one on the x-axis. If it is a set of separate categories with no in-between values — soil types, brands, locations — use a bar graph. If it is a number that could take any value in a range — time, temperature, height, mass — use a line graph. A quick test: ask whether a point halfway between two x-values would mean anything. If yes, a line graph works; if no, use bars.
- What is the difference between correlation and causation in simple terms?
- Correlation means two things change together. Causation means one thing makes the other happen. Every correlation has at least three possible explanations: the first thing causes the second, the second causes the first, or a hidden third factor causes both. Only a controlled experiment, where you change one variable and hold the rest constant, gives you good evidence for causation. Observational data can point you toward a question worth testing, but it cannot answer the cause question on its own.
- Should I delete a data point that does not fit the pattern?
- No. Report it, label it as an outlier, and describe the trend of the remaining data separately. If you know a specific reason it is wrong — you bumped the table, the timer restarted, you misread the scale — write that reason down and explain why you are excluding it. Deleting data with no explanation is not honest science, and outliers sometimes point to a real effect you had not expected.
- How long does a conclusion need to be?
- Length matters less than coverage. A strong conclusion can be four or five sentences as long as it does three jobs: states specific evidence with actual numbers, directly answers the question you started with, and names at least one thing the evidence does not show. Adding a sentence of reasoning that connects the evidence to science you already know makes it stronger. Vague sentences like "the experiment worked" or "the data proved my hypothesis" do none of those jobs.
Learn this with a teacher, not a page
The Crimsora tutor teaches Reading Data, Graphs & Drawing Conclusions live — explaining on a whiteboard, asking you questions, and adapting to where you get stuck.