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Consultation paper

Presenting data in graphs, charts and tables —

science subjects

This edition: November 2015 (version 1.0)

© Scottish Qualifications Authority 2015

Contents

Presenting data in graphs, charts and tables — science subjects ....................... 1

Rationale ......................................................................................................... 1

Mark allocation ................................................................................................ 1

General marking principles for graphs, charts and tables in both internal and

external assessment ........................................................................................ 3

Biology and Human Biology ............................................................................. 5

Chemistry ...................................................................................................... 10

Physics .......................................................................................................... 12

November 2015 version 1.0

SQA Consultation paper: Presenting data — science subjects 1

Consultation paper

Presenting data in graphs, charts and tables —

science subjects This guidance document relates to internal and external assessment of National Qualifications in

Biology, Chemistry, Environmental Science, Human Biology, Physics and Science. It provides

teachers, lecturers and assessors with advice and guidance on the use of different formats for the

presentation of data.

A graph is a visual representation of data. Some graphs can be used to determine the relationship

or trend between variables. Values not measured can be estimated from some graphs using

extrapolation (extending the best fit line beyond either the first or last point plotted) or interpolation

(estimating a value between two plotted points).

Rationale

As far as possible skills taught in science should be transferable across science subjects to ensure

that learners studying more than one science are not disadvantaged. To ensure consistency the

general marking principles provided in this document should be applied to graphs, charts and

tables across the sciences.

Question Paper

Within question papers SQA has responsibility for ensuring that the type of data used allow

learners to readily recognise the type of presentation format and that the skills required for

interpreting data are appropriate to the format used.

Assignments/Projects (National 4–Advanced Higher)

As part of Course assessment for National Qualifications learners are required to select data

and present it in an appropriate format. The formats used should be in line with the principles

in this document. If particular data is commonly presented in a format other than a format

suggested in this document, then the commonly used format should also be acceptable.

Mark allocation

Question Paper

Not all graph questions will have the same mark allocation. The number of marks allocated

will depend upon:

what the learner has to complete in terms of scales, labels, plotting, joining of points,

best fit line and identifying rogue points

the complexity of the data


SQA Consultation paper: Presenting data 2

Assignments/Projects (National 4–Advanced Higher)

Specific Marking Instructions will provide detailed mark allocations.

Different types of data are represented using different types of graph or chart. It is important

that:

the correct type of graph is drawn

a line appropriate for the data is drawn

only skills appropriate to the graph type are assessed

Format Type of data Skills that can be

assessed

Line graph

line of best

fit

(a straight

line or

curve)

Two continuous variables where a

change in the dependent variable

is caused by a change in the

independent variable.

presenting information

selecting information

determining a

mathematical relationship

identifying a trend

extrapolation

interpolation

calculating a gradient

calculate the area under

the line without using

calculus

explain changes in shape

point-to-

point

(adjacent

points

joined by a

ruler)

or

Stick/spike

graph

Two continuous variables where a

change in the dependent variable

is not caused by the independent

variable.

or

Where confounding variables may

be masking any mathematical

relationship.

or

One continuous variable and one

discrete variable.



identifying a trend

explain changes in shape

calculation of the area

under a graph line (eg

displacement/time or

velocity/time) without

using calculus

Bar chart

or Pie

chart

One continuous variable and one categoric

variable.



Histogram One continuous variable or classes with a

numerical range and the frequency, percentage

or number.



examine the distribution

of the data



General marking principles for graphs, charts and tables in both

internal and external assessment

Graphs

Axis and plotting

Each axis should be labelled with the variable name and unit.

Abbreviations for axis labels are acceptable where it is clear what the abbreviation

means.

If SI units are abbreviated then only the standard abbreviation is acceptable. For non

SI units, symbols or abbreviations in normal use (eg min for minute) will also be

acceptable.

If a scientific multiplier is used, it may be included with the axis label or units.

Spelling errors should not be penalised unless it is not clear what the learner means

or if the spelling is too close to another word, eg ‘angle of defraction’ is not

acceptable as it is not clear if this means diffraction or refraction.

Each axis should be marked with an appropriate scale. The scale should be of a size

that allows the points to be easily read or use at least half of the graph paper or grid.

A common zero at the origin is acceptable if appropriate for the data.

If a zero is not included on the scale this will not be penalised if the location of the

zero is implied by the rest of the scale.

Major and minor grid lines should be included to allow the accuracy of processing to

be checked.

A scale break or a scale not starting at zero is acceptable if appropriate for the data.

Points/bars/spikes should be plotted such that the marker can check the accuracy,

with a tolerance of half the smallest division.

If all points/bars/spikes are on major or minor grid lines then the detailed Marking

Instructions may indicate that no tolerance will be applied.

Line graphs

Normally the independent variable should be plotted on the X (horizontal) axis and

the dependent variable on the Y (vertical) axis.

Plotted points should be clearly distinguishable from the graph grid lines and the line

drawn.

If points should be joined or a line drawn then this must be appropriate for the data

being presented.

For data requiring a line of best fit the following will be accepted at the level

indicated:

— National 4 — accept a reasonable attempt at a line of best fit or point-to-point,

ie adjacent data points joined with a ruler

— National 5 — accept a reasonable attempt at a line of best fit (not point-to-

point)

— Higher — accept a good attempt at a line of best fit

— Advanced Higher — accept a good attempt at a line of best fit



When multiple lines are plotted then it should be clear, either from labelling or the use

of a key, what each line represents.

Interpolation and extrapolation are only appropriate for a line of best fit.

Bar charts

Bar charts may be drawn either vertically or horizontally depending upon the number

of categories and length or complexity of the category labels.

Normally the X axis represents the different categories and so has no scale. As the

categories are discrete, a gap should normally be left between the bars.

A common zero at the origin is not normally acceptable.

Pie charts

All lines should originate from the central point.

A 2° tolerance is acceptable unless ‘tick marks’ are given and the divisions are

exactly on the ‘tick marks’.

Histograms

The X axis should have a continuous scale or be divided into classes with a

numerical range.

As the X axis is continuous there should normally be no gaps between the columns

representing the different classes.

The Y axis should be the frequency, numbers or percentage in each category.

Tables

Column headings should contain the variable name and units.

Abbreviations for headings are acceptable where it is clear what the abbreviation

means. Spelling errors will not be penalised unless it is not clear what the learner

means.

If SI units are abbreviated then only the standard abbreviation is acceptable. For non

SI units, symbols or abbreviations in normal use (eg min for minute) will also be

acceptable.

Where a unit is not given in the heading but is given in the column it must be given

for every value.

Values should be quoted to the same number of significant figures as the measured

data. However a tolerance of one fewer or up to two more is acceptable.

Figures can be converted to scientific notation.

The scientific multiplier may be included with the units in the table heading.



Biology and Human Biology

Line graphs

Continuous variables are normally measured on a linear numerical scale. When the range of

values for one variable is large a logarithmic scale can be used.

Most commonly in Biology we would expect candidates to be dealing with quantitative data

where:

It is not certain (or known) that the change in the dependent variable is caused by the

independent variable

or

Confounding variables or random variation may be masking any mathematical relationship.

The presentation format for this type of data is a line graph with straight lines joining the

points.

Example: point to point



When there are sufficient data points to be confident in the relationship or because, from

theory, there is good reason to believe that the intermediate values fall on the line, the

appropriate presentation format is a line of best fit.

Example: line of best fit

Bar graphs

Bar graphs are used to display and compare the number, frequency or other measure for

different discrete categories of data. The length of each bar is proportional to the value it

represents. The bars can be drawn either vertically or horizontally depending upon the

number of categories and length or complexity of the category labels.

Bar graphs can also be used for more complex comparisons of data with grouped bar

graphs and stacked bar graphs. Grouped bar graphs are a way of showing information about

different sub-groups of the main categories where a separate bar represents each of the

sub-groups. In stacked bar graphs the bars representing the sub-groups are placed on top of

each other to make a single column.

Example: vertical (column) bar graph



Example: horizontal bar graph

Example: grouped bar graph

Example: stacked bar graph



Pie charts

A pie chart shows data where the categories are proportions of a whole. The ‘pie’ is divided

into segments that represent this proportion. This is done by dividing the angles at the

centre. The entire pie represents the total data set and each segment of the pie is a

particular category within the whole.

Example

Histograms

A histogram is a graphical representation of the distribution of numerical data. It is an

estimate of the probability distribution of a quantitative variable. Due to the large number of

possible values the data are grouped to reduce the number of data points.

Example

Behaviour of pigs in an enclosure



Tables

Candidates will often present raw, final or processed data in a table.

Examples



Chemistry

Line graphs

Line graphs are used to process/analyse data consisting of two continuous numerical

variables where a change in the independent variable causes a change in the dependent

variable.

When the range of values for a variable is large, a logarithmic scale can be used.

Due to uncertainty in measurements, all data points will not normally lie on a single straight

line or curve. By examining the scatter of points candidates are expected to form a

judgement as to whether a best fit straight line or curve is appropriate. No line should be

drawn if the data points do not support either a straight line or curve.

Line graphs can be used to determine the relationship between the variables, and, by

calculating the gradient of a straight line, to determine the value of a constant.

0 2 4 6 8 10 12

Time / mins

40

35

30

25

20

15

10

5

0

Vo

lum

e o

f H

yd

rog

en / c

m3



Bar charts

Bar charts are used to present data consisting of one variable that is continuous and one

that is discontinuous.

The trend in a bar chart can be illustrated by drawing a trend line, which is a line of best fit

where the data points are at the centre of the top of each bar.

More complex data can be presented using a grouped bar chart.

1 2 3 4 5 6

Number of carbon atoms

En

tha

lpy o

f com

bustio

n / k

J m

ol-1

4000

3500

3000

2500

2000

1500

1000

500

0

80

60

40

20

0

Pe

rce

nta

ge b

y v

olu

me

/ %

Crude oil source

Saudi Light

North Sea Brent

South Louisiana

Beryl

Naphthenes

Aromatics

Paraffins



Physics

Line graphs

Line graphs are used to process/analyse data consisting of two continuous numerical

variables where a change in the independent variable causes a change in the dependent

variable.

When the range of values for a variable is large, a logarithmic scale can be used. An

example of this would be a Hertzsprung-Russell diagram in Higher or Advanced Higher

question papers.

Due to uncertainty in measurements, all data points will not normally lie on a single straight

line or curve. By examining the scatter of points candidates are expected to form a

judgement as to whether a best fit straight line or curve is appropriate. No line should be

drawn if the data points do not support either a straight line or curve.

Line graphs are commonly used to determine the relationship between the variables, and, by

calculating the gradient of a straight line, to determine the value of a constant.

0 20 40 60 80 100 120 140 160

Distance / mm

4·0

3·5

3·0

2·5

2·0

1·5

1·0

0·5

0

Po

ten

tia

l d

iffe

rence/k

V



Sketching graphs

Candidates may be asked to sketch a graph or sketch an additional line on to a graph using

data given in the question. To do this accurately candidates may be required to mark certain

values on the axes and indicate a scale by having two values on the axis, one of which is

usually the origin. The specific requirements of sketch graphs are made clear in the

question, and acceptable responses are detailed in the relevant Marking Instructions.

0·00 0·20 0·40 0·60 0·80 1·00 1·20 1·40

time / s

0·0

-5·0

-10·0

-15·0

-20·0

back emf / V



Bar charts

Bar charts are used to present data consisting of one variable that is continuous and one

that is discontinuous.

The trend in a bar chart can be illustrated by drawing a trend line, which is a line of best fit

where the data points are at the centre of the top of each bar.

1 2 3 4 5 6

Number of elastics used to accelerate trolley

Acce

lera

tio

n o

f tr

olle

y / m

s-2

0·8

0·7

0·6

0·5

0·4

0·3

0·2

0·1

0

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