Consultation paper Presenting data in graphs, charts and tables science subjects


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1 Consultation paper Presenting data in graphs, charts and tables science subjects This edition: November 2015 (version 1.0) Scottish Qualifications Authority 2015
2 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 Physics... 12
3 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 science subjects 1
4 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 Bar chart or Pie chart Histogram pointtopoint (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. One continuous variable and one categoric variable. One continuous variable or classes with a numerical range and the frequency, percentage or number. presenting information selecting information identifying a trend explain changes in shape calculation of the area under a graph line (eg displacement/time or velocity/time) without using calculus presenting information selecting information presenting information selecting information examine the distribution of the data SQA Consultation paper: Presenting data 2
5 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 pointtopoint, ie adjacent data points joined with a ruler National 5 accept a reasonable attempt at a line of best fit (not pointtopoint) Higher accept a good attempt at a line of best fit Advanced Higher accept a good attempt at a line of best fit SQA Consultation paper: Presenting data 3
6 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. SQA Consultation paper: Presenting data 4
7 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 SQA Consultation paper: Presenting data 5
8 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 subgroups of the main categories where a separate bar represents each of the subgroups. In stacked bar graphs the bars representing the subgroups are placed on top of each other to make a single column. Example: vertical (column) bar graph SQA Consultation paper: Presenting data 6
9 Example: horizontal bar graph Example: grouped bar graph Example: stacked bar graph SQA Consultation paper: Presenting data 7
10 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 Behaviour of pigs in an enclosure 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 SQA Consultation paper: Presenting data 8
11 Tables Candidates will often present raw, final or processed data in a table. Examples SQA Consultation paper: Presenting data 9
12 Volume of Hydrogen / cm 3 November 2015 version 1.0 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 Time / mins SQA Consultation paper: Presenting data 10
13 Percentage by volume / % Enthalpy of combustion / kj mol 1 November 2015 version 1.0 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 Number of carbon atoms More complex data can be presented using a grouped bar chart Paraffins Naphthenes 40 Aromatics 20 0 Saudi Light North Sea Brent South Louisiana Beryl Crude oil source SQA Consultation paper: Presenting data 11
14 Potential difference/kv November 2015 version 1.0 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 HertzsprungRussell 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 Distance / mm SQA Consultation paper: Presenting data 12
15 0 0 time / s back emf / 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. SQA Consultation paper: Presenting data 13
16 Acceleration of trolley / m s 2 November 2015 version 1.0 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 Number of elastics used to accelerate trolley SQA Consultation paper: Presenting data 14
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