KS3 Science Study Pack: Data and Graph Skills

Key Knowledge

What scientific data is and why it matters

Scientific data is information collected from observations or measurements. In science, data is important because it gives evidence. Evidence helps scientists decide whether an idea is supported by results, needs changing, or needs testing again.

A measurement is a value found using equipment, such as a thermometer reading of 24 degrees C, a mass of 50 g, or a time of 12 s. An observation is something noticed using the senses or simple equipment, such as "the solution turned cloudy" or "the plant leaves were pale green".

Data can be:

• Raw data: the original results recorded during an investigation.
• Processed data: data that has been changed in a useful way, such as by calculating a mean, drawing a graph, or converting results into a percentage.

For example, if a student measures the time taken for salt to dissolve at different temperatures, the times they record are raw data. When they calculate the mean time for each temperature and plot a line graph, they have processed the data so it is easier to interpret.

Scientists use data to:

• compare results,
• reveal patterns,
• test predictions,
• check whether a method was reliable,
• communicate findings clearly,
• write conclusions based on evidence.

Good data handling is a major part of working scientifically. It links practical work to scientific thinking. A table of numbers is not enough on its own; scientists must organise, process, interpret, and evaluate those numbers.

Variables and results tables

A variable is something that can change in an investigation.

The three main types of variable are:

• Independent variable: the variable deliberately changed.
• Dependent variable: the variable measured or observed.
• Control variables: variables kept the same to make the test fair.

Example investigation: A student tests how ramp height affects the distance a toy car travels.

Variable type	Variable in this investigation	Why it matters
Independent variable	Ramp height (cm)	This is what the student changes.
Dependent variable	Distance travelled by the car (cm)	This is what the student measures.
Control variables	Same car, same ramp surface, same starting point	These help make the test fair.

Another example:

Investigation	Independent variable	Dependent variable	Control variables
Testing how light intensity affects plant growth	Light intensity (lux)	Plant height after 10 days (cm)	Plant species, water volume, soil type, time grown
Testing how water temperature affects dissolving time	Water temperature (degrees C)	Time for salt to dissolve (s)	Mass of salt, volume of water, stirring method

Results tables organise data so that it can be checked and understood. A good results table has:

• a clear title,
• headings for each variable,
• units in the headings,
• repeat measurements where appropriate,
• an average column when repeats are used,
• neat rows and columns.

Units should go in the column heading, not repeated in every data cell. For example, write Time taken (s) as the heading, then put 12, 13, and 11 in the cells.

Title: Time taken for salt to dissolve at different water temperatures

+-------------------------+--------------+--------------+--------------+----------+
| Water temperature       | Repeat 1     | Repeat 2     | Repeat 3     | Mean     |
| (degrees C)             | time (s)     | time (s)     | time (s)     | time (s) |
+-------------------------+--------------+--------------+--------------+----------+
| 20                      | 85           | 82           | 84           | 84       |
| 40                      | 52           | 50           | 53           | 52       |
| 60                      | 31           | 30           | 32           | 31       |
+-------------------------+--------------+--------------+--------------+----------+

This structure makes it clear what was changed, what was measured, and how the final values were calculated.

Choosing the right graph type

Graphs help scientists see patterns more easily than a table alone. The correct graph depends on the type of data.

Graph type	Best for	Example	Common mistake
Bar chart	Categoric or discrete groups	Type of surface and distance travelled	Drawing bars touching
Line graph	Continuous variables and change	Time and temperature	Using uneven scale intervals
Scatter graph	Correlation between paired measurements	Height and arm span	Claiming correlation proves causation

Categoric data is data in named groups, such as type of material, colour of light, fertiliser type, or surface type. Discrete data is data that is counted in separate values, such as number of leaves or number of woodlice. A bar chart is usually best for categoric or simple discrete groups.

Continuous data can take any value on a scale, such as time, temperature, distance, length, mass, concentration, or light intensity. A line graph is usually best when one continuous variable changes with another.

A scatter graph is used for pairs of measurements when looking for a relationship or correlation. For example, a class might compare hours of exercise per week with resting pulse rate. Each point represents one person.

Pie charts are rarely the best choice for scientific investigation results. A pie chart is useful for showing parts of a whole, such as the percentage of gases in air, but it is not usually useful for showing how one variable affects another.

What kind of data do you have?
|
+-- Categories or groups? --> Bar chart
|
+-- Continuous change? ----> Line graph
|
+-- Paired measurements? --> Scatter graph

Key graph features

Feature	What it means	Why it matters
Axis label	The variable shown on an axis	Tells the reader what was measured
Unit	The measurement unit	Makes values meaningful
Scale	The value steps on an axis	Allows accurate plotting and reading
Point	A plotted pair of values	Shows one result
Line of best fit	A line showing the general pattern	Helps show correlation

A graph should usually include:

• a clear title,
• an x-axis label,
• a y-axis label,
• units for both axes if needed,
• a sensible scale,
• accurately plotted data,
• neat bars, points, or lines.

The x-axis is the horizontal axis. It usually shows the independent variable. The y-axis is the vertical axis. It usually shows the dependent variable.

                   Title: Temperature of water as it cools

Temperature
(degrees C)
 90 |  x
 80 |    x
 70 |       x
 60 |          x
 50 |             x
 40 |                x
    +--------------------------------
      0    2    4    6    8    10
                 Time (min)

Labelled y-axis + unit      Plotted points      Labelled x-axis + unit
Scale increases evenly       Trend line may show the pattern

Drawing accurate bar charts

A bar chart is used for categories or groups. The bars should have equal width, and there should be gaps between them because the categories are separate.

Example: A student tests how different surfaces affect the distance a toy car travels.

Surface type	Distance travelled (cm)
Carpet	45
Wood	82
Plastic	96
Rubber	38

The independent variable is surface type. This is categoric, so a bar chart is suitable.

Distance
(cm)
100 |              █
 90 |              █
 80 |       █      █
 70 |       █      █
 60 |       █      █
 50 | █     █      █
 40 | █     █      █      █
 30 | █     █      █      █
 20 | █     █      █      █
 10 | █     █      █      █
  0 +------------------------------
      Carpet Wood Plastic Rubber
             Surface type

Bars have gaps because surface type is categoric.

A good bar chart should include:

• a title, such as Distance travelled by a toy car on different surfaces,
• category labels on the x-axis,
• measured values on the y-axis,
• units on the y-axis,
• bars with equal width,
• bars with gaps,
• accurate bar heights.

From the example, plastic has the tallest bar at 96 cm, and rubber has the shortest bar at 38 cm. The toy car travelled 58 cm further on plastic than on rubber.

Drawing accurate line graphs

A line graph is used when the independent variable is continuous and the investigation is about change across a scale.

Example: A student measures the temperature of hot water every 2 minutes as it cools.

Time (min)	Temperature (degrees C)
0	80
2	70
4	62
6	56
8	52
10	50

Both time and temperature are continuous. A line graph is suitable because it shows how temperature changes over time.

Temperature
(degrees C)
 80 | x
 75 |  \
 70 |   x
 65 |    \
 60 |      x
 55 |        x
 50 |          x---x
    +--------------------
      0  2  4  6  8  10
           Time (min)

The points are plotted from the table.
The line shows the cooling trend.

To draw a line graph:

1. Write a clear title.
2. Put the independent variable on the x-axis.
3. Put the dependent variable on the y-axis.
4. Add units to both axis labels.
5. Choose a sensible scale.
6. Plot each coordinate accurately.
7. Join points with straight line segments or draw a smooth curve if the pattern is gradual and suitable.

Straight line segments are often acceptable at KS3 because they show the measured values clearly. A smooth curve can be suitable for a cooling curve if the points suggest a smooth change. Do not force a line through points if they are scattered randomly.

Drawing and interpreting scatter graphs

A scatter graph is used to look for a relationship between two measured variables. Each point shows a pair of measurements.

Example: A group compares hours of exercise per week with resting pulse rate.

Student	Exercise per week (hours)	Resting pulse rate (beats per minute)
A	1	82
B	2	78
C	3	75
D	4	72
E	5	70
F	6	67
G	7	66

As exercise increases, resting pulse rate tends to decrease. This is a negative correlation. It does not prove that exercise alone caused the lower pulse rate, because other factors such as age, health, stress, or measurement method may also affect pulse rate.

Resting pulse rate
(beats per minute)
 85 | x
 80 |   x
 75 |     x
 70 |        x  x
 65 |             x  x
    +----------------------
      1  2  3  4  5  6  7
       Exercise per week (hours)

Negative correlation: as exercise increases, pulse rate tends to decrease.

A line of best fit can be drawn on a scatter graph if there is a clear pattern. It should:

• pass through the general pattern of points,
• have roughly balanced points on either side,
• not simply join dot to dot,
• not need to pass through every point.

Plant height
(cm)
 30 |             x
 25 |          x
 20 |       x
 15 |    x
 10 | x
    +--------------------
      0  20 40 60 80 100
       Light intensity (lux)

Positive correlation: plant height tends to increase as light intensity increases.
Line of best fit would rise through the middle of the points.

Reading scales and values from graphs

A scale is the set of value steps on an axis. Equal spaces on an axis must represent equal increases. It is not acceptable to use uneven gaps just because the labels are correct.

Good scales often use simple intervals such as:

• 1,
• 2,
• 5,
• 10,
• 20,
• 50,

A graph should use most of the graph paper without making the scale confusing. Not every graph has to start at zero. Starting at zero is often sensible, especially for bar charts, but a non-zero start can be acceptable if small differences need to be seen clearly. The scale must be clear and not misleading.

Example scale:

Temperature (degrees C)

40 |----|----|----|----| 50
   42   44   46   48

Each small step is 2 degrees C.
The value halfway between 44 and 46 is 45 degrees C.

Another example:

Distance (cm)

0 |----|----|----|----| 20
  5   10   15

Each small step is 5 cm.
A point three small steps above 0 is 15 cm.

Interpolation means estimating a value between measured points. For example, if water was 70 degrees C at 2 minutes and 62 degrees C at 4 minutes, an estimated value at 3 minutes might be about 66 degrees C.

Extrapolation means estimating beyond the measured data. This should be done cautiously because the pattern may change outside the tested range. If a cooling graph has only been measured to 10 minutes, predicting the temperature at 60 minutes may be unreliable.

Calculating averages from repeat results

An average is a value that represents a set of results. At KS3, the most common average is the mean.

To calculate the mean:

1. Add the values.
2. Divide by the number of values.
3. Include the unit.

Example:

Three repeat results are 12 s, 13 s, and 11 s.

Mean = (12 + 13 + 11) / 3

Mean = 36 / 3

Mean = 12 s

Other averages include:

• Median: the middle value when numbers are in order.
• Mode: the most common value.

The range is the difference between the largest and smallest values. It is not an average, but it shows how spread out results are.

Example:

Values: 11 s, 12 s, 13 s

Range = 13 s - 11 s = 2 s

A small range between repeat readings suggests the results are repeatable. A large range may suggest measurement errors, uncontrolled variables, or natural variation.

Identifying and dealing with anomalies

An anomaly is a result that does not fit the pattern or is very different from other repeat results. An anomaly might be caused by:

• measurement error,
• equipment error,
• method error,
• an uncontrolled variable,
• a recording mistake,
• a real but unusual result.

Anomalies should not automatically be removed. Scientists should investigate them first. A result should only be ignored if there is a justified scientific reason.

Example repeat results:

Trial	Time taken (s)
Repeat 1	18
Repeat 2	19
Repeat 3	45

The value 45 s may be anomalous because it is much higher than 18 s and 19 s.

Mean with the anomaly:

(18 + 19 + 45) / 3 = 82 / 3 = 27.3 s

Mean without the anomaly:

(18 + 19) / 2 = 37 / 2 = 18.5 s

It may be reasonable to exclude 45 s if the student recorded that the stop clock was started late or the method went wrong. If there is no evidence of an error, the student should be careful about removing it. They could repeat the measurement to check.

When writing about anomalies, be clear:

• "The result of 45 s was treated as an anomaly because the stop clock was started late."
• "The mean was calculated without the anomaly."
• "The result was kept because there was no evidence that the measurement was wrong."

Describing trends and correlations

A trend is the general pattern in data. A trend can be:

• increasing,
• decreasing,
• no clear pattern,
• changing quickly,
• changing slowly,
• levelling off,
• rising then falling.

A correlation is a relationship between two variables. A scatter graph can show:

• Positive correlation: as one variable increases, the other tends to increase.
• Negative correlation: as one variable increases, the other tends to decrease.
• No correlation: there is no clear relationship.

Correlation does not automatically prove causation. Causation means one thing directly causes another. Two variables can be correlated because of another factor or by coincidence.

Weak trend description:

"The graph goes up."

Stronger trend description:

"As the mass on the spring increased from 100 g to 500 g, the extension increased from 2 cm to 10 cm. This shows a positive relationship between mass and extension over the range tested."

Strong trend descriptions use values from the data. Values are important because they prove that the conclusion is based on evidence.

Writing strong scientific conclusions

A conclusion should answer the investigation question using evidence from the data. It should not just describe what happened.

Part of conclusion	Question to ask	Example sentence starter
Answer	What did the investigation show?	The results show that...
Trend	How did the dependent variable change?	As ... increased, ...
Evidence	Which values prove it?	For example, ... changed from ... to ...
Limitation	How could the data be improved?	One limitation was...

Weak conclusion:

"The temperature changed."

Improved conclusion:

"The results show that the water cooled over time. As time increased from 0 min to 10 min, the temperature decreased from 80 degrees C to 50 degrees C. The temperature fell fastest at the start, dropping by 10 degrees C in the first 2 minutes. One limitation is that the temperature was only measured every 2 minutes, so more frequent readings would give a more detailed cooling curve."

A strong conclusion:

• answers the question,
• describes the trend,
• uses numerical evidence,
• includes units,
• mentions anomalies if relevant,
• does not make claims beyond the data.

Evaluating the quality of data

Evaluation means judging how good the data and method were.

Important words:

• Accuracy: how close a measurement is to the true value.
• Precision: how close repeated measurements are to each other, or how small the measurement intervals are.
• Repeatability: how similar results are when the same person repeats the method using the same equipment.
• Reliability: how trustworthy the results are, often improved by repeats, consistent patterns, and similar results from other groups or methods.

Reliable does not mean the same as accurate. A set of results can be repeatable but still inaccurate if the measuring equipment is wrongly calibrated.

Ways to improve data quality include:

• take more repeats,
• calculate a mean,
• test more values of the independent variable,
• control variables more carefully,
• use equipment with smaller scale divisions,
• use a wider range if it is safe and suitable,
• repeat anomalous results,
• record units and headings clearly,
• use a suitable graph type and scale.

Worked Examples

Worked example 1: Choosing a graph type

Investigation A: A student tests how the type of material affects the time taken for ice to melt.

• Independent variable: type of material.
• Data type: categoric.
• Best graph: bar chart.
• Reason: the materials are separate categories, such as cotton, foil, wool, and plastic. Bars should have gaps.

Investigation B: A student records temperature every minute as water cools.

• Independent variable: time.
• Data type: continuous.
• Best graph: line graph.
• Reason: time and temperature are measured on continuous scales, and the investigation shows change over time.

Investigation C: A class compares hand span and reaction time.

• Variables: hand span and reaction time are paired measurements for each student.
• Best graph: scatter graph.
• Reason: the class is looking for correlation between two measured variables.

Worked example 2: Setting up a results table

Messy list of results:

"At 20 degrees C, salt dissolved in 85 s, 82 s, and 84 s. At 40 degrees C, it took 52 s, 50 s, and 53 s. At 60 degrees C, it took 31 s, 30 s, and 32 s."

Improved table:

Water temperature (degrees C)	Repeat 1 time (s)	Repeat 2 time (s)	Repeat 3 time (s)	Mean time (s)
20	85	82	84	84
40	52	50	53	52
60	31	30	32	31

Why this table is better:

• The independent variable is in the first column.
• The dependent variable is time taken.
• Units are in headings.
• Repeat results are clearly shown.
• The mean column processes the raw data.

Worked example 3: Calculating a mean

Repeat results: 12 s, 13 s, 11 s

Step 1: Add the results.

12 + 13 + 11 = 36

Step 2: Divide by the number of results.

36 / 3 = 12

Step 3: Add the unit.

Mean time = 12 s

If one value is anomalous, do not remove it automatically. Check whether there is a reason, such as a method error. If it is excluded, state this clearly.

Worked example 4: Handling an anomaly

Repeat results: 18 s, 19 s, 45 s

The result 45 s may be anomalous because it is far from the other two values.

Mean with the anomaly:

(18 + 19 + 45) / 3 = 27.3 s

Mean without the anomaly:

(18 + 19) / 2 = 18.5 s

A good scientific explanation:

"The result of 45 s appears anomalous because it is much higher than the other repeats, 18 s and 19 s. I would not remove it unless there was evidence of a problem, such as the stop clock being started late. The best improvement would be to repeat the measurement."

Worked example 5: Reading a graph scale

Look at this axis:

Mass (g)

0 |----|----|----|----| 100
  25   50   75

The labelled values show that four equal spaces represent 100 g. Therefore each small space represents 25 g.

If a point is halfway between 50 g and 75 g, the value is about 62.5 g.

Look at this axis:

Temperature (degrees C)

10 |----|----|----|----| 30
   15   20   25

Each step is 5 degrees C. A point one step above 20 degrees C is 25 degrees C.

Worked example 6: Plotting a line graph

Dataset:

Time (min)	Temperature (degrees C)
0	80
2	70
4	62
6	56
8	52
10	50

Steps:

1. Title: Temperature of water as it cools.
2. x-axis: Time (min).
3. y-axis: Temperature (degrees C).
4. Scale: x-axis from 0 to 10 in steps of 2; y-axis from 50 to 80 in steps of 5 or 10.
5. Plot points: (0, 80), (2, 70), (4, 62), (6, 56), (8, 52), (10, 50).
6. Draw a neat line showing the cooling trend.

Worked example 7: Interpreting a line graph

Using the cooling data above, the temperature falls fastest at the start. From 0 min to 2 min, it falls from 80 degrees C to 70 degrees C, a drop of 10 degrees C. From 8 min to 10 min, it falls from 52 degrees C to 50 degrees C, a drop of only 2 degrees C. This shows that the cooling rate decreases and the graph begins to level off.

Worked example 8: Interpreting a scatter graph

Dataset:

Hours of exercise per week	Resting pulse rate (beats per minute)
1	82
2	78
3	75
4	72
5	70
6	67
7	66

The scatter graph would show negative correlation because the resting pulse rate tends to decrease as exercise increases. For example, at 1 hour of exercise the pulse rate is 82 beats per minute, while at 7 hours it is 66 beats per minute.

This does not prove that exercise caused the lower pulse rate. Other variables may be involved, such as age, fitness, health, or how carefully the pulse was measured.

Worked example 9: Writing a stronger conclusion

Weak conclusion:

"The plant grew more."

Stronger conclusion:

"The results show that plant height increased as light intensity increased. At 20 lux, the mean plant height was 8 cm, while at 100 lux it was 24 cm. This suggests a positive relationship between light intensity and plant growth over the range tested. One limitation is that only five light intensities were tested, so testing more values would make the pattern more reliable."

Key Vocabulary

Term	KS3 definition	Example
Data	Information collected from observations or measurements	Temperatures recorded every minute
Evidence	Data used to support a scientific idea or conclusion	A graph showing temperature decreased
Result	A measurement or observation from an investigation	42 cm travelled by a car
Measurement	A value found using equipment	25 degrees C on a thermometer
Observation	Something noticed during an investigation	The solution became cloudy
Variable	Something that can change	Temperature, time, mass
Independent variable	The variable deliberately changed	Ramp height
Dependent variable	The variable measured	Distance travelled
Control variable	A variable kept the same	Same toy car each time
Raw data	Original results before processing	Three repeat times
Processed data	Data changed to make it more useful	A mean or graph
Repeat	Doing a measurement again	Measuring dissolving time three times
Mean	Add values and divide by how many values there are	(12 + 13 + 11) / 3 = 12 s
Median	Middle value when values are in order	Median of 3, 5, 8 is 5
Mode	Most common value	Mode of 2, 4, 4, 7 is 4
Range	Difference between highest and lowest values	20 cm - 12 cm = 8 cm
Average	A value representing a set of data	Mean height of plants
Anomaly	A result that does not fit the pattern	45 s when repeats are 18 s and 19 s
Trend	General pattern in data	Temperature decreases over time
Pattern	A regular relationship or change	More mass gives more extension
Correlation	A relationship between two variables	Taller people may have larger arm spans
Positive correlation	Both variables tend to increase together	More light, taller plants
Negative correlation	One variable increases as the other decreases	More exercise, lower resting pulse
No correlation	No clear relationship	Shoe size and reaction time
Causation	One variable directly causes a change in another	Heating water causes its temperature to rise
Scale	Value steps on an axis	0, 10, 20, 30
Axis	A reference line on a graph	x-axis or y-axis
x-axis	Horizontal graph axis	Usually independent variable
y-axis	Vertical graph axis	Usually dependent variable
Unit	The measurement label	cm, s, g, degrees C
Coordinate	A pair of values for plotting a point	(4 min, 62 degrees C)
Bar chart	Graph for categories or groups	Surface type and distance
Line graph	Graph for continuous change	Temperature over time
Scatter graph	Graph for paired measurements	Hand span and reaction time
Line of best fit	Line showing the general pattern on a scatter graph	A rising line through plant height points
Interpolation	Estimating between measured points	Estimating temperature at 3 minutes
Extrapolation	Estimating beyond measured data	Predicting temperature after 1 hour
Conclusion	A statement answering the investigation question using evidence	"As time increased, temperature decreased..."
Accuracy	Closeness to the true value	A thermometer reading near the real temperature
Precision	Closeness of repeats or detail of measurement	Readings all near 20.1 cm
Repeatability	Similarity when the same method is repeated	Three distances of 42, 43, 42 cm
Reliability	Trustworthiness of results	Repeats and a clear pattern support reliability

Common Misconceptions

Wrong idea	Why it is wrong	Correct idea
All graphs should start at zero.	A non-zero start can help show small differences, if it is clear.	Zero is often useful, but the scale must be fair and not misleading.
Anomalies should always be removed.	A strange result may be real or may need checking.	Investigate anomalies and only exclude them with a justified reason.
A line graph is always better than a bar chart.	Graph choice depends on data type.	Use bar charts for categories and line graphs for continuous change.
Bars should touch in a bar chart.	Touching bars suggest continuous data.	Bars for categories should have gaps.
A line of best fit must go through every point.	Real data often has scatter.	A best-fit line shows the overall pattern and balances points.
Correlation proves causation.	Two variables may be linked because of another factor.	Correlation suggests a relationship but does not prove cause.
The average is always the correct answer.	Averages can hide variation and be affected by anomalies.	Check the spread of results and look for anomalies.
More decimal places means a result is more accurate.	Extra digits do not help if the measurement is wrong.	Accuracy means close to the true value.
Reliable means the same as accurate.	Consistent results can still be wrong.	Reliable means trustworthy or consistent; accurate means close to true.
If a graph goes up, the conclusion is complete.	It does not use enough evidence.	Quote values and explain the trend clearly.
A table is complete if it has numbers.	Numbers without headings or units are unclear.	A good table needs headings, units, repeats, and clear organisation.
Uneven gaps on an axis are acceptable if the labels are correct.	Uneven gaps distort the graph.	Equal spaces must represent equal changes.

Real-World Examples

Biology examples

Plant growth at different light levels can be shown with a line graph if light intensity is measured in lux. If different light colours are compared, a bar chart may be better because colour is categoric.

Pulse rate before and after exercise can be shown in a bar chart if the categories are "before exercise" and "after exercise". If pulse rate is measured every minute during recovery, a line graph is better because time is continuous.

Reaction time compared with amount of sleep can be shown with a scatter graph because each person has a pair of measurements: sleep time and reaction time.

The number of woodlice in light and dark areas can be shown with a bar chart because the areas are categories.

Chemistry examples

Temperature change during a simple classroom reaction can be shown with a line graph if temperature is measured every 30 seconds.

The time taken for salt to dissolve at different water temperatures can be shown with a line graph because temperature is continuous.

pH values of household substances can be shown with a bar chart because the substances are categories, such as lemon juice, soap solution, and tap water.

The volume of gas produced over time in a safe classroom reaction can be shown with a line graph because time and volume are continuous.

Physics examples

Distance travelled by a toy car down ramps of different heights can be shown with a line graph if ramp height is measured in centimetres. If the surfaces are carpet, wood, plastic, and rubber, a bar chart is better.

A cooling curve for hot water is a line graph because it shows temperature changing over time.

The extension of a spring when different masses are added is usually a line graph because mass and extension are continuous.

Sound level at different distances from a source is a line graph because distance is continuous.

Diagram Interpretation

Labelled graph layout

                     Graph title
        Effect of mass on spring extension

Extension
(cm)       y-axis label + unit
 12 |                         x
 10 |                    x
  8 |               x
  6 |          x
  4 |     x
  2 | x
  0 +--------------------------------
      0   100 200 300 400 500 600
                Mass (g)
                x-axis label + unit

Each x is a plotted point.
Equal spaces on each axis show equal increases.

Questions to ask when interpreting this diagram:

• What is the independent variable?
• What is the dependent variable?
• Are units shown?
• Does the scale increase evenly?
• What trend is shown?
• Which values support the trend?

Results-table structure

+----------------------+-----------+-----------+-----------+----------+
| Independent variable | Repeat 1  | Repeat 2  | Repeat 3  | Mean     |
| with unit            | result    | result    | result    | result   |
+----------------------+-----------+-----------+-----------+----------+
| Value 1              |           |           |           |          |
| Value 2              |           |           |           |          |
| Value 3              |           |           |           |          |
+----------------------+-----------+-----------+-----------+----------+

This table reminds you to include the variable, repeats, and an average column.

Data and Graph Practice Tasks

Task 1: Results table, variables, and means

A student investigates how water temperature affects the time taken for sugar to dissolve.

Water temperature	Repeat 1 time	Repeat 2 time	Repeat 3 time	Mean time
20	92	88	90
40	54	56	55
60	31	30	32

Questions:

1. Add suitable units to the column headings.
2. Identify the independent variable.
3. Identify the dependent variable.
4. Suggest two control variables.
5. Calculate the mean time for each temperature.
6. Describe the trend using values.

Model answers:

1. Water temperature (degrees C), Repeat 1 time (s), Repeat 2 time (s), Repeat 3 time (s), Mean time (s).
2. Water temperature.
3. Time taken for sugar to dissolve.
4. Same mass of sugar and same volume of water. Other suitable answers include same stirring method or same type of sugar.
5. At 20 degrees C: (92 + 88 + 90) / 3 = 90 s. At 40 degrees C: (54 + 56 + 55) / 3 = 55 s. At 60 degrees C: (31 + 30 + 32) / 3 = 31 s.
6. As water temperature increased from 20 degrees C to 60 degrees C, the mean dissolving time decreased from 90 s to 31 s.

Task 2: Graph choice

Choose the best graph type for each investigation and explain why.

Investigation	Best graph	Reason
Testing how surface type affects distance travelled by a toy car
Measuring temperature every minute as water cools
Comparing hand span and reaction time for students
Measuring gas volume every 20 seconds during a reaction
Comparing pH values of different household substances

Model answers:

Investigation	Best graph	Reason
Testing how surface type affects distance travelled by a toy car	Bar chart	Surface type is categoric.
Measuring temperature every minute as water cools	Line graph	Time and temperature are continuous, and the graph shows change.
Comparing hand span and reaction time for students	Scatter graph	It uses paired measurements and looks for correlation.
Measuring gas volume every 20 seconds during a reaction	Line graph	Time and gas volume are continuous.
Comparing pH values of different household substances	Bar chart	The substances are categories.

Task 3: Bar chart interpretation

A toy car is released down a ramp onto different surfaces.

Surface type	Mean distance travelled (cm)
Carpet	40
Cardboard	65
Wood	88
Sandpaper	32

Questions:

1. Which surface allowed the car to travel the furthest?
2. Which surface gave the shortest distance?
3. How much further did the car travel on wood than on carpet?
4. Why is a bar chart suitable?
5. What should the y-axis label be?

Model answers:

1. Wood, with a mean distance of 88 cm.
2. Sandpaper, with a mean distance of 32 cm.
3. 88 cm - 40 cm = 48 cm.
4. Surface type is categoric, so separate bars with gaps are suitable.
5. Mean distance travelled (cm).

Task 4: Line graph interpretation

Water is left to cool in a beaker.

Time (min)	Temperature (degrees C)
0	82
2	72
4	64
6	59
8	56
10	54

Questions:

1. What is the temperature at 4 min?
2. During which 2-minute section does the temperature fall fastest?
3. How much does the temperature fall from 0 min to 10 min?
4. Describe the trend using values.
5. Estimate the temperature at 5 min.

Model answers:

1. 64 degrees C.
2. From 0 min to 2 min, because it falls from 82 degrees C to 72 degrees C, a drop of 10 degrees C.
3. 82 degrees C - 54 degrees C = 28 degrees C.
4. The temperature decreases over time. It falls from 82 degrees C at 0 min to 54 degrees C at 10 min, and the decrease becomes slower near the end.
5. About 61 or 62 degrees C, using interpolation between 64 degrees C at 4 min and 59 degrees C at 6 min.

Task 5: Scatter graph and correlation

Students measure light intensity and plant height after 14 days.

Light intensity (lux)	Plant height (cm)
20	7
40	12
60	16
80	20
100	23
120	24

Questions:

1. What type of correlation is shown?
2. What evidence supports this?
3. Should a line of best fit go through every point?
4. Does this prove that light intensity is the only cause of plant height?
5. Suggest one control variable.

Model answers:

1. Positive correlation.
2. As light intensity increases from 20 lux to 120 lux, plant height increases from 7 cm to 24 cm.
3. No. It should show the general pattern with points roughly balanced on either side.
4. No. It suggests a relationship, but plant height may also be affected by water, soil, species, or temperature.
5. Same plant species, same water volume, same soil type, or same growing time.

Task 6: Anomaly task

A student measures how far a toy car travels from the same ramp height.

Repeat	Distance travelled (cm)
1	74
2	76
3	43
4	75

Questions:

1. Which result may be anomalous?
2. Why might it be an anomaly?
3. Calculate the mean including all four results.
4. Calculate the mean without the possible anomaly.
5. What further check would help?

Model answers:

1. 43 cm.
2. It is much lower than the other results, which are 74 cm, 76 cm, and 75 cm.
3. (74 + 76 + 43 + 75) / 4 = 268 / 4 = 67 cm.
4. (74 + 76 + 75) / 3 = 225 / 3 = 75 cm.
5. Repeat the measurement and check whether the car hit an obstacle, was released differently, or the distance was recorded incorrectly.

Task 7: Conclusion task

Use this data about spring extension:

Mass (g)	Extension (cm)
100	2
200	4
300	6
400	8
500	10

Write a conclusion using this structure:

• answer the question,
• describe the trend,
• quote evidence,
• mention one limitation or improvement.

Model answer:

"The results show that increasing the mass increased the extension of the spring. As mass increased from 100 g to 500 g, extension increased from 2 cm to 10 cm. This shows a positive relationship over the range tested. One improvement would be to repeat each mass and calculate a mean extension to improve reliability."

Task 8: Scale-reading task

Read these axes.

A: Distance (cm)
0 |----|----|----|----| 40
  10   20   30

B: Time (s)
20 |----|----|----|----| 28
   22   24   26

Questions:

1. What is each small step worth on axis A?
2. What value is halfway between 20 cm and 30 cm?
3. What is each small step worth on axis B?
4. What value is halfway between 24 s and 26 s?

Model answers:

1. 10 cm.
2. 25 cm.
3. 2 s.
4. 25 s.

Task 9: Data quality task

A student tests only two ramp heights and does one repeat for each height.

Questions:

1. Why is this data not very reliable?
2. Suggest two improvements.
3. Which improvement helps repeatability?
4. Which improvement helps show the trend more clearly?

Model answers:

1. There are too few results, and no repeats to check consistency.
2. Test more ramp heights and take at least three repeats at each height.
3. Repeats help check repeatability.
4. Testing more values of the independent variable helps show the trend more clearly.

Exam-Style Questions

Multiple-choice questions

1. Which graph is best for comparing the time taken for ice to melt on different materials?

A. Line graph
B. Bar chart
C. Scatter graph
D. Pie chart

Answer: B. A bar chart is best because material type is categoric.

2. Which statement about a line of best fit is correct?

A. It must pass through every point.
B. It should show the overall pattern.
C. It is only used on bar charts.
D. It proves one variable caused another.

Answer: B. A line of best fit shows the general pattern and should balance the points.

3. A student records 10 cm, 11 cm, and 12 cm. What is the mean?

A. 10 cm
B. 11 cm
C. 12 cm
D. 33 cm

Answer: B. (10 + 11 + 12) / 3 = 11 cm.

4. Which word means "close to the true value"?

A. Reliable
B. Repeatable
C. Accurate
D. Categoric

Answer: C. Accuracy means closeness to the true value.

5. Why should bars usually have gaps in a bar chart?

A. To show the scale starts at zero.
B. To show the groups are separate categories.
C. To make the graph look larger.
D. To show a line of best fit.

Answer: B. Bar charts often show separate categories, so the bars should have gaps.

FillBlank questions

1. The variable deliberately changed is the ______ variable.

Answer: independent

2. The variable measured is the ______ variable.

Answer: dependent

3. A result that does not fit the pattern is called an ______.

Answer: anomaly

4. Estimating a value between measured points is called ______.

Answer: interpolation

5. A relationship where both variables tend to increase together is called ______ correlation.

Answer: positive

6. Equal spaces on an axis must represent equal ______.

Answer: increases

Short-answer questions

1. A student tests how different fertilisers affect plant height. Which graph should be used?

Model answer: A bar chart, because fertiliser type is categoric.

2. A student measures temperature every minute for 20 minutes. Which graph should be used?

Model answer: A line graph, because time and temperature are continuous variables and the graph shows change over time.

3. Explain why a mean can be affected by an anomaly.

Model answer: The mean uses all the values, so one value that is much higher or lower can pull the mean away from the typical results.

4. What is wrong with putting cm in every cell of a results table?

Model answer: Units should be in the column heading, such as Distance (cm), so the table is clearer and less cluttered.

5. Why is extrapolation less certain than interpolation?

Model answer: Extrapolation estimates beyond the measured data, where the pattern may change. Interpolation estimates between measured points, so it is usually more supported by evidence.

Spot the mistake questions

1. A graph axis is labelled 0, 5, 10, 30, 35 with equal spaces between labels. What is wrong?

Model answer: The scale is uneven. Equal spaces must represent equal increases, but the jump from 10 to 30 is much larger than the others.

2. A student draws a line graph for different types of surfaces. What is wrong?

Model answer: Surface type is categoric, so a bar chart would usually be better. A line graph suggests continuous data.

3. A student removes an anomaly because "it makes the graph look better". What is wrong?

Model answer: Anomalies should only be excluded if there is a justified scientific reason, such as a known measurement or method error.

4. A conclusion says, "The graph went up, so my prediction was right." What is missing?

Model answer: It needs the scientific trend, values from the data, units, and a clear link to the investigation question.

Longer 6-8 mark question

A student investigates how water temperature affects the time taken for a salt to dissolve. The student uses the same mass of salt and the same volume of water each time.

Water temperature (degrees C)	Repeat 1 time (s)	Repeat 2 time (s)	Repeat 3 time (s)
20	88	90	89
30	70	69	71
40	54	92	53
50	41	40	42
60	31	30	32

Question:

Calculate or use suitable mean values, identify any anomaly, describe the trend using evidence, and write a conclusion about how water temperature affects dissolving time. Include one improvement to the data collection.

Model answer:

At 20 degrees C, the mean time is (88 + 90 + 89) / 3 = 89 s. At 30 degrees C, the mean is (70 + 69 + 71) / 3 = 70 s. At 40 degrees C, 92 s appears anomalous because it is much higher than 54 s and 53 s. If there was a justified method error, such as the salt not being stirred in the same way, it could be excluded; the mean without it is (54 + 53) / 2 = 53.5 s. At 50 degrees C, the mean is (41 + 40 + 42) / 3 = 41 s. At 60 degrees C, the mean is (31 + 30 + 32) / 3 = 31 s.

The results show that as water temperature increased, the time taken for the salt to dissolve decreased. For example, the mean time decreased from 89 s at 20 degrees C to 31 s at 60 degrees C. This supports the conclusion that higher water temperature makes the salt dissolve faster over the range tested. One improvement would be to repeat the 40 degrees C result to check the anomaly and improve reliability.

How marks are earned:

• Correct mean calculations with units.
• Identification of 92 s as a possible anomaly.
• Justified treatment of the anomaly.
• Clear trend described before explanation.
• Numerical evidence quoted.
• Conclusion answers the investigation question.
• Improvement linked to reliability or repeatability.

Model Answers: Graph-Plotting Features

When asked to plot a bar chart, a good answer should include:

• a title linked to the investigation,
• categories on the x-axis,
• the measured variable on the y-axis,
• units in the y-axis label,
• a sensible y-axis scale,
• bars of equal width,
• gaps between bars,
• accurate bar heights.

When asked to plot a line graph, a good answer should include:

• a title,
• independent variable on the x-axis,
• dependent variable on the y-axis,
• units on both axes,
• equal scale intervals,
• points plotted accurately as coordinates,
• points joined with straight line segments or a suitable smooth curve.

When asked to plot a scatter graph, a good answer should include:

• a title,
• one measured variable on each axis,
• units where needed,
• accurately plotted paired points,
• no dot-to-dot joining,
• a line of best fit if there is a clear correlation,
• a description of positive, negative, or no correlation.

Revision Checklist

Use this checklist before a quiz or assessment.

Skill	I can do this
Explain that data is evidence from observations or measurements
Identify raw data and processed data
Identify independent, dependent, and control variables
Set up a results table with headings and units
Put units in headings, not every data cell
Explain when to use a bar chart
Explain when to use a line graph
Explain when to use a scatter graph
Explain why pie charts are rarely best for investigation results
Choose a sensible graph scale
Explain why a graph does not always have to start at zero
Plot coordinates accurately
Draw bars with equal widths and gaps
Draw a line graph with labelled axes and units
Draw a line of best fit on a scatter graph
Read values from graph scales
Interpolate between measured points
Avoid overclaiming when extrapolating
Calculate a mean from repeat results
Explain median, mode, range, and average
Identify anomalies
Decide whether an anomaly should be included or excluded
Describe increasing, decreasing, and levelling-off trends
Describe positive, negative, and no correlation
Explain why correlation does not prove causation
Write a conclusion using values and units
Evaluate accuracy, precision, repeatability, and reliability
Suggest improvements to data quality

Final Quick Review

Data and graph skills help scientists move from results to conclusions. A results table organises raw data. A graph reveals patterns. A mean can summarise repeat results, but anomalies must be checked carefully. A conclusion should answer the investigation question, describe the trend, quote evidence with units, and mention limitations where relevant. The best graph type depends on the data: bar charts for categories, line graphs for continuous change, and scatter graphs for paired measurements and correlation.