4 Analyzing Data and Drawing Conclusions

Organize measurements

Record observations and measurements in a clearly labeled table. Give the table a specific title, identify what each row and column represents, and include units in the headings. Keep the original measurements so they can be checked later; for repeated trials, show each result as well as any calculated summary.

For the seedling investigation, the recorded results are:

• At $0$ hours of light per day, the three trial heights are $3\text{ cm}$, $4\text{ cm}$, and $5\text{ cm}$, with a mean of $4\text{ cm}$.

• At $4$ hours of light per day, the trial heights are $6\text{ cm}$, $7\text{ cm}$, and $8\text{ cm}$, with a mean of $7\text{ cm}$.

• At $8$ hours of light per day, the trial heights are $9\text{ cm}$, $10\text{ cm}$, and $11\text{ cm}$, with a mean of $10\text{ cm}$.

Use consistent precision when recording results. For example, recording all heights to the nearest centimeter makes comparisons clearer.

Choose and read graphs

Choose a graph that fits the comparison being made. A line graph shows how a measured quantity changes across an ordered scale, such as time or light exposure. A bar graph compares amounts across separate categories, such as different fertilizer types. A scatterplot shows paired numerical measurements and helps reveal whether they vary together.

For the seedling investigation, plot light exposure on the horizontal axis and mean height on the vertical axis. Label both axes with units, select a scale that shows the data clearly, and give the graph a descriptive title. The plotted means are $(0,4)$, $(4,7)$, and $(8,10)$, where the first value is light exposure in hours and the second is mean height in centimeters. These results show that average height increased as light exposure increased in this set of results.

A graph can make a pattern visible, but it does not explain by itself why the pattern occurred.

Summarize results and variation

Summaries describe different features of a set of measurements. The mean gives an average and is calculated as

The median is the middle value after measurements are ordered. The range shows the span of the observations and is calculated as

In the seedling example, the mean heights at the three light levels are $4\text{ cm}$, $7\text{ cm}$, and $10\text{ cm}$. Each set of trial heights has a range of $2\text{ cm}$. Reporting individual trials alongside a mean shows that repeated measurements varied, even though the overall pattern was consistent. Tables, graphs, and statistical summaries can be used together to reveal patterns and relationships.

Evaluate patterns and uncertainty

Check whether a pattern is consistent across trials, whether any results are unusual, and how much measurements vary. Consider possible sources of uncertainty, including limited measurement precision, different starting conditions, or too few trials. Repeated trials can help show whether a result is consistent, while careful tools and procedures can reduce some measurement problems. Uncertainty does not automatically make data useless; it helps define how confident a conclusion should be.

Consider the limits of the investigation as well. In the seedling example, water, temperature, or soil could also affect growth. Unless these factors were controlled, the results alone do not show that light caused the difference. A relationship between two measured variables is not, by itself, proof of cause and effect. Measurement error and sample selection are also limitations to consider when interpreting data.

Draw conclusions from evidence

A strong conclusion answers the investigation question and connects a claim to specific evidence. It distinguishes what was observed from what is inferred and mentions important limits or uncertainty.

For example: “In this investigation, seedlings exposed to more daily light had greater mean heights after two weeks: the means were $4\text{ cm}$ at $0$ hours, $7\text{ cm}$ at $4$ hours, and $10\text{ cm}$ at $8$ hours. This pattern is consistent with a relationship between light exposure and height, but further controlled trials would be needed to establish whether light caused the difference.”

Keep conclusions specific to the measured results and avoid claiming more than the investigation supports. New or conflicting data may require a conclusion to be revised; scientific explanations are evaluated against evidence, not protected from it.

• evidence-based conclusion