1. Data Processing and Analysis
Photo credit: © 2011 Vanessa Nel, Shutterstock.com
Data Processing and Analysis

3. Planning an investigation
As part of your GCSE Science course you will be assessed on your ability to plan, carry out, analyse the results of and evaluate investigations.
You will be expected to present and analyse results in order to reach a clear conclusion.
What should you consider when analysing your results and coming to a conclusion?

4. Presenting results
Results from most investigations should be presented in a table, which should be drawn up before the investigation is carried out.
the table should be simple and easy to read
the independent variable should be in the left-hand column
there must be a column for each measurement you plan to take, including any repeats, and a column for any value you will calculate, like an average
Teacher notes
The values of any control variables are best listed under the table as adding columns for them can make tables unwieldy.
the table headings should give the name of the variable and its units – there should be no units next to your results
results must have an appropriate number of decimal points.

5. Presenting results: tables
Oliver investigated the relationship between the length of nichrome wire and its resistance.
a column for each variable and calculated value
independent variable and unit
10.0
6.1, 6.1
6.1
0.81, 0.80
0.81
7.53
30.0
6.0, 6.1
0.28, 0.27
0.28
21.8
50.0
6.0, 6.0
6.0
0.16, 0.15
0.16
37.5
70.0
6.1, 6.0
0.12, 0.14
0.13
46.9
90.0
5.9, 6.0
0.09, 0.10
0.10
60.0
100.0
6.0, 5.9
0.08, 0.08
0.08
75.0
length (cm)
V (V)
average V (V)
I (A)
average I (A)
R ()
repeats
consistency in number of decimal places

6. Presenting results: tables 2
James investigated the relationship between the temperature of sodium thiosulfate and the time it took to turn cloudy with hydrochloric acid. What mistakes has he made in his table?
no unit
no quantity
Temperature
Time taken for solution to go cloudy
Average 15
85 s, 91 s, 88 s
88 s
20.0
76 s, 72 s, 73 s s 25
68.3 s, 69 s, 67 s s
30.00
62 s, 63 s, 62 s s 35
59 s, 58 s, 60 s
59 s
units should be in column headings, not table body
inconsistent
decimal places
inconsistent decimal places

7. Reliability: calculating averages
To ensure reliability, you should repeat your investigation several times and compare results.
You then need to identify and discard any anomalous results or outliers. These are values that don’t appear to fall within the expected pattern or range of measurements.
Finally, calculate the average of your results: add up all the individual data values then divide by the total number of values.
Teacher notes
Students need to recognise when results should be left out of the average because they are anomalous. For example: 59, 58 and 60 are consistent values but 59, 42 and 60 are not. The 42 should not be included in the average.
average =
sum of all data values
total number of data values

8. Calculating averages Teacher notes
Students should be reminded to identify and discard outliers/anomalies before calculating the average.

10. Presenting results: graphs
Drawing a graph makes it easier to spot trends and patterns in results. However, it must be neat, clear and easy to interpret.
Label the axes with the names of the independent and dependent variables and any units.
Put the independent variable on the horizontal axis unless you are told otherwise.
Choose scales that let your graph fill the paper. You do not need to start at zero.
Don’t forget to add a title that shows what the graph is about.

11. What type of graph?

12. Pie charts
A pie chart uses sectors of a circle to display categoric data.
For example, a class survey of eye colour produced the following results:
Eye colour
Number
Angle at centre
brown
blue
green
other 11
(11/27) × 360° = 147° 9
(9/27) × 360° = 120° 4
(4/27) × 360° = 53° 3
(3/27) × 360° = 40°

13. poor scale: wasted space
Mistakes with graphs
The graph shows the relationship between the acid concentration and the volume of CO2 produced in 1 minute with marble chips. What three mistakes can you spot?
no units
poor scale: wasted space
points should be drawn by a line of best fit or smooth curve, whichever is most appropriate.
Teacher notes
In this example it is appropriate to start both axes at zero, but this is not always necessary. Starting at a higher value often lets the graph fill more of the paper.

14. Graph analysis Teacher notes
When interpolating graphs, students should be encouraged to draw lines on the graph to show how they got their readings.

16. Reaching a conclusion Teacher notes
Students should recognise linear and directly proportional relationships.
A straight line shows that there is a linear relationship between the variables. In other words: when one variable increases by a set amount it always has the same effect on the other variable.
A straight line that passes through zero shows that one variable is directly proportional to the other. In other words: when one doubles, the other doubles.

17. Evaluating investigations
After finishing your investigation you need to carry out an evaluation to decide how certain you are of your conclusion.
You need to consider the reliability and validity of your results and whether they were as you expected.
Photo credit: © 2011 Vanessa Nel, Shutterstock.com
Based on your evaluation you might decide that you have confidence in your results and conclusion or you may decide that further investigations are needed. You may even identify the reasons for the investigation not working as you expected.

18. Evaluation: an example
Oliver investigated how the pulling force of a falling mass affected the acceleration of a trolley.
His results lie close to a straight line, which suggests they are reliable.
However, the graph suggests that the trolley would still accelerate if there was no mass. Are his results reliable?
Teacher notes
These results all lie close to the line of best fit so the variation in the data is likely to be caused by random errors in the measurements. Repeating the readings and calculating a new mean can reduce the effect of these errors.
If a point is a long way from the line or curve of best fit it could be anomalous. Students should try to identify a possible error that could have made the measurement too high or too low.

19. Evaluating investigations
Teacher notes
Q1: If the effect of changing the acid concentration is tested using a very exothermic reaction, it is difficult to keep the temperature constant. Students should recognise instances like this, where the quality of the evidence does not allow a conclusion to be made with confidence. They are expected to evaluate the data collection method and explain any weaknesses in the evidence.
Q2: This is an example of a systematic error because using acidic water affects all the results. Students should recognise that repeating the readings will not reduce the effect of a systematic error.
Q3: In this case it is not possible to draw an accurate curve through the points because the optimum temperature is not clear. Students should recognise that extra evidence is needed. Photosynthesis was fastest at 25oC, so additional temperatures around this value should be tested.

20. Glossary Teacher notes
anomaly – A value that doesn’t appear to fall within the expected pattern or range of measurements. Also known as an outlier.
average – A single value that typifies a set of measurements. The most common type of average is the mean, which is equal to the sum of all the values in a data set divided by the total number of values in that set.
bar chart – A chart used when the independent variable is categoric or ordered. It compares results for different values of the independent variable without showing a definite relationship.
categoric – A variable that can be described with labels and which cannot be ranked. For example, the eye colours of students in a class.
causal link – A link to describe when a change in one variable is caused by a change in another variable.
continuous – A variable that can take any numerical value. For example, the temperature of water in a beaker.
correlation – A relationship between two variables in an investigation. A correlation does not necessarily indicate a causal link. Correlations can be identified from graphs or charts. If the gradient (slope) of a graph is positive (i.e. it slopes upwards) there is a positive correlation. If the gradient is negative (i.e. it slopes downwards) there is a negative correlation.
dependent – A variable that is measured during an investigation for each change of the independent variable.
discrete – A type of categoric variable that can only be whole numbers (integers). For example, the value of a slotted mass.
fair test – A test in which only the independent variable has been allowed to affect the dependent variable.
independent – The variable that is changed during an investigation to see what effect it has on the dependent variable.
line graph – A graph is used to present results if the independent variable is continuous and a causal link with the dependent variable has been established.
ordered – A type of categoric variable that produces data that can be ranked. For example, the size of marble chips in a rates of reaction experiment might be large, medium or small.
outlier – See anomaly.
pie chart – A chart that uses a circle split into sectors to present categorical data. The size of each sector is proportional to the value of the data.
range – The difference between the smallest and largest values in a set of measurements. It is not the number of measurements taken.
reliability – The extent to which measurements of a quantity remain consistent after repeated measurements under the same conditions. The more consistent results are, the more reliable they are.
scattergram – A graph used when investigating two naturally changing variables to see if there is a correlation between them.
validity – The extent to which data or conclusions have been obtained from an investigation that has been suitably designed to test the proposed hypothesis. For laboratory-based investigations, validity depends on performing a fair test.
variable – A quantity or characteristic that can be changed and have different values. There are several types of variable.