IaS2 What conclusions can we make from data?

Twenty First Century Science - Combined Science B - J260 · Cambridge OCR GCSE (9-1) · 7 min read · Updated: 27 Aug 2026

Ideas about Science (IaS2): What Conclusions Can We Make from Data?

Welcome to one of the most useful toolkits in science! Have you ever wondered how scientists turn a messy page of laboratory numbers into groundbreaking discoveries, life-saving medicines, or climate models? It all comes down to data analysis.

In this chapter, you will learn how to organize, calculate, graph, and evaluate scientific data. These skills are essential across Biology, Chemistry, and Physics papers in OCR Combined Science B (Twenty First Century Science J260). Let's take it step by step!

1. Units, Prefixes, and Presenting Data

Presenting Data Clearly

When collecting data in an experiment, recording numbers clearly ensures anyone can interpret your results accurately:

Data Tables: Every table column must have a clear heading containing both the quantity being measured and the unit. In OCR exams, write this using a solidus (slash) or brackets: e.g., Time / s, Distance (m), or Volume / \(\text{cm}^3\).
Presentation Formats: You need to translate data between different formats, including numerical tables, frequency tables, bar charts, histograms, and scatter or line graphs.

Standard SI Units

Scientists around the world use standard SI (International System) units so they can share and compare findings without confusion:

Mass: kilogram (\(\text{kg}\)), gram (\(\text{g}\)), milligram (\(\text{mg}\))
Length / Distance: kilometer (\(\text{km}\)), meter (\(\text{m}\)), millimeter (\(\text{mm}\))
Time: second (\(\text{s}\))
Energy: joule (\(\text{J}\)), kilojoule (\(\text{kJ}\))
Force: newton (\(\text{N}\))
Electric Current: ampere (\(\text{A}\))
Potential Difference: volt (\(\text{V}\))
Volume: cubic centimeter (\(\text{cm}^3\)), cubic decimeter (\(\text{dm}^3\))

Note: Always use standard IUPAC chemical names (e.g., sodium chloride, copper(II) sulfate) when naming chemical substances.

Metric Prefixes and Powers of 10

When values are extremely large or tiny, we use metric prefixes. You must memorize these prefixes and their powers of 10:

tera (\(\text{T}\)): \(10^{12}\) (1,000,000,000,000)
giga (\(\text{G}\)): \(10^9\) (1,000,000,000)
mega (\(\text{M}\)): \(10^6\) (1,000,000)
kilo (\(\text{k}\)): \(10^3\) (1,000)
centi (\(\text{c}\)): \(10^{-2}\) (\(\frac{1}{100}\) or 0.01)
milli (\(\text{m}\)): \(10^{-3}\) (\(\frac{1}{1000}\) or 0.001)
micro (\(\mu\)): \(10^{-6}\) (0.000001)
nano (\(\text{n}\)): \(10^{-9}\) (0.000000001)

Unit Conversion Tip: Always check your units before substituting them into physics formulas!

To convert \(\text{kJ}\) to \(\text{J}\), multiply by \(1000\) (or \(10^3\)).
To convert \(\text{g}\) to \(\text{kg}\), divide by \(1000\).
To convert \(\text{cm}^3\) to \(\text{dm}^3\), divide by \(1000\) (since \(1\text{ dm}^3 = 1000\text{ cm}^3\)).

Key Takeaway: Always label table headings with quantity and unit (e.g., Energy / \(\text{kJ}\)), and convert prefixed numbers to base units before calculating.

2. Processing Data: Means, Ranges, and Significant Figures

The Best Estimate: Calculating the Mean

When you repeat measurements in an experiment, the arithmetic mean represents your best estimate of the true value:

\(\text{Mean} = \frac{\sum \text{values}}{\text{number of values}}\)

Spread and Range

Repeated measurements are rarely identical. The range tells you the spread of your data:

Range: The interval between the lowest and highest measured values.
It can be calculated as: \(\text{Range} = \text{maximum value} - \text{minimum value}\), or stated as an interval: \([\text{minimum value}, \text{maximum value}]\).
A set of repeat measurements provides a spread or range within which the true value probably lies.

Significant Figures

Don't write down a long string of decimals from your calculator! Calculated answers must be rounded to an appropriate number of significant figures, matching the precision of the raw data provided in the question.

Example: If your raw balance readings are \(2.4\text{ g}\) and \(2.6\text{ g}\) (2 significant figures), your calculated mean should be quoted as \(2.5\text{ g}\), not \(2.500\text{ g}\).

Handling Outliers (Anomalies)

An outlier (or anomalous result) is a data point that deviates significantly from the pattern of repeats.

Crucial OCR Exam Rule: You must treat a suspected outlier as valid data unless there is a clear, identified reason to reject it.

Valid reasons to reject an outlier: You know you spilled some solution, misread the scale, or started the stopwatch late. In this case, exclude it when calculating the mean.
No identified error? If there is no clear procedural error or contamination, the outlier must remain included in your calculations.

Key Takeaway: The arithmetic mean is the best estimate of the true value. Never discard an outlier without a specific, justified reason!

3. Graphing, Trends, and Linear Relationships

Plotting Rules for Science Exams

Axes: Put the independent variable (the one you change) on the horizontal \(x\)-axis, and the dependent variable (the one you measure) on the vertical \(y\)-axis.
Scale: Choose regular, linear scales (e.g., in steps of 1, 2, 5, or 10). Your graph must fill more than half of the available grid space.
Plotting Points: Mark points accurately with a sharp pencil using a small cross (\(\times\)) or an encircled dot (\(\odot\)).

Lines of Best Fit and Range Bars

Line of Best Fit: Draw a single, smooth curve or straight line that balances points evenly on both sides. Ignore confirmed outliers. Never draw dot-to-dot jagged lines!
Do not force your line through the origin \((0,0)\) unless the data and scientific theory confirm it should start at zero.
Range Bars: Vertical error or range bars are drawn at each data point to visually display the spread of repeats and illustrate experimental uncertainty.

Analyzing Linear Relationships: \(y = mx + c\)

When a graph forms a straight line, it shows a linear relationship defined by:

\(y = mx + c\)

\(m\) = the gradient (slope of the line)
\(c\) = the \(y\)-intercept (the value of \(y\) where the line crosses the vertical axis)

Calculating the Gradient

To calculate the gradient of a straight line:

\(m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}\)

Examiner Tip: When calculating a gradient on an exam:

Draw a large right-angled triangle on your line of best fit (spanning at least half the length of the line).
Pick coordinates directly from the line of best fit, not from the raw data table.
Calculate \(\frac{\text{change in } y}{\text{change in } x}\).

Rate of Change for Curves (Drawing Tangents)

If your graph is a curve, the rate of change is constantly changing. To find the rate at any specific point:

Place a ruler against the curve at that exact point so it forms a straight tangent (touching the curve without crossing through it).
Draw the tangent line.
Calculate the gradient of this tangent: \(\frac{\Delta y}{\Delta x}\).

Interpolation vs. Extrapolation

Interpolation: Estimating a value inside the range of measured data points (very reliable).
Extrapolation: Extending the line of best fit beyond the measured data to predict trends (less reliable, as the trend might change).

Key Takeaway: Use large gradient triangles (\(\ge 50\%\) of the line) with points chosen directly from the best-fit line. For curves, draw a tangent to find the rate of change.

4. Evaluating Data Quality: Errors and Reliability

Accuracy vs. Precision

Don't worry if these sound similar at first! In science, they have very specific definitions:

Accuracy: How close a measured value is to the true value.
Precision: How close repeat measurements are to each other (reflected by a narrow spread/range).

The Dartboard Analogy:

If all your darts hit close to the bullseye, your throws are both accurate and precise.
If all your darts land tightly clustered in the top-left corner far from the bullseye, they are precise, but not accurate.
If your darts are scattered all over the board, they have poor precision and poor accuracy.

Repeatability vs. Reproducibility

Repeatability: The precision obtained when the same investigator repeats the experiment using the same method and equipment in the same lab.
Reproducibility: The precision obtained when the investigation is repeated by different investigators or using different equipment/techniques.

Types of Experimental Errors

Random Errors: Unpredictable fluctuations caused by human reaction time, slight temperature changes, or estimating values between scale divisions.
How to reduce them: Take multiple repeat readings and calculate a mean.
Systematic Errors: Flaws in equipment or experimental design that shift all measurements in one direction by a consistent amount (e.g., a top-pan balance that reads \(+0.5\text{ g}\) before anything is placed on it — known as a zero error).
Important: Systematic errors cannot be eliminated by taking repeats and calculating a mean! You must fix the apparatus or calibrate the zero setting.

Key Takeaway: Random errors cause data spread and are reduced by taking means. Systematic errors shift all data equally and require recalibrating equipment.

Quick Revision Checklist

Can you write table headings correctly (e.g., Distance / \(\text{m}\))?
Do you know the prefixes from nano (\(10^{-9}\)) to tera (\(10^{12}\))?
Can you calculate the arithmetic mean and state the range?
Do you know the rule for outliers (only exclude if there is a clear, identified reason)?
Can you calculate a gradient using \(m = \frac{\Delta y}{\Delta x}\) with a large triangle?
Can you construct a tangent to find the gradient of a curve?
Can you clearly explain the difference between accuracy, precision, repeatability, and reproducibility?

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

How should column headings in a scientific data table be written?

Every column heading must include both the quantity being measured and the unit, separated by a solidus or brackets (e.g., Time / \(\text{s}\) or Distance (\(\text{m}\))).

What are the standard SI metric prefixes from nano to tera and their corresponding powers of 10?

\(\text{nano (n)} = 10^{-9}\), \(\text{micro (}\mu\text{)} = 10^{-6}\), \(\text{milli (m)} = 10^{-3}\), \(\text{centi (c)} = 10^{-2}\), \(\text{kilo (k)} = 10^3\), \(\text{mega (M)} = 10^6\), \(\text{giga (G)} = 10^9\), and \(\text{tera (T)} = 10^{12}\).

What does the arithmetic mean represent in an experiment, and how is it calculated?

The arithmetic mean is the best estimate of the true value and is calculated using \(\text{Mean} = \frac{\sum \text{values}}{\text{number of values}}\).

What is the range of a set of repeat measurements?

The range is the spread of data between the lowest and highest values: \(\text{Range} = \text{maximum value} - \text{minimum value}\), or stated as an interval \([\text{minimum}, \text{maximum}]\).

When is it permissible to discard an outlier (anomalous result) in science exams?

Only when there is a clear, identified procedural error or reason (such as a spill or timing mistake); otherwise, it must remain included.

How do you calculate the gradient of a straight line of best fit on a graph?

Using \(m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}\), drawing a large triangle on the line covering at least half its length.

How do you determine the rate of change at a specific point on a curved graph?

Draw a straight tangent touching the curve at that exact point and calculate the gradient of the tangent (\(\frac{\Delta y}{\Delta x}\)).

What is the difference between interpolation and extrapolation?

Interpolation estimates values within the range of measured data, whereas extrapolation extends the line of best fit beyond measured data points.

What is the difference between accuracy and precision?

Accuracy describes how close a measurement is to the true value, whereas precision describes how close repeated measurements are to each other.

What is the difference between repeatability and reproducibility?

Repeatability is precision when the same investigator repeats the test with identical equipment; reproducibility is precision when different investigators or methods are used.

What is the difference between random errors and systematic errors, and how are they addressed?

Random errors cause unpredictable scatter and are reduced by taking repeats and calculating a mean; systematic errors shift all readings equally and require recalibrating equipment or fixing the method.

Ready to test yourself?

Turn these notes into exam-style practice. Get unlimited AI questions on this topic with instant marking and explanations.

Practise This Topic

More Twenty First Century Science - Combined Science B - J260 chapters

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

Put These Notes into Practice

Reading the notes is a great start. Now practise with unlimited AI-generated questions and get instant feedback. 100,000+ students are already improving their grades.

Start Practising Now View Pricing

Done reading? Test yourself with AI practice questions

Practise This Topic Now