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Wf - 2003 Statistical Coursework There are more vowels used in a page written out in French rather than English. Girls are better at maths than boys

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Wf - 2003 Assessing the task Statistical coursework is marked under three headings: Specifying the problem and planning Collecting, processing and representing the data Interpreting and discussing the results

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Wf - 2003 1. Specifying the problem and planning This strand is about choosing a problem and deciding what needs to be done, then doing it. The strand requires you to provide clear aims, consider the collection of data, identify practical problems and explain how you might overcome them. For the higher marks you need to decide upon a suitable sampling method, explain what steps were taken to avoid possible bias and provide a well structured report.

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Wf - 2003 2. Collecting, processing and representing the data This strand is about collecting data and using the most appropriate statistical techniques and calculations to process and represent the data. Diagrams should be appropriate and calculations mostly correct. For the higher marks you will need to accurately use higher level statistical techniques and calculations from the higher tier GCSE syllabus content.

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Wf - 2003 3. Interpreting and discussing the results This strand is about commenting, summarising and interpreting your data. Your discussion should link back to the original problem and provide an evaluation of the work undertaken. For the higher marks you will need to provide sophisticated and rigorous interpretations of your data and provide an analysis of how significant your findings are.

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Wf - 2003 Getting started – setting up your hypothesis Moderator comment: Your statistical task must always start with a ‘hypothesis’ where you state exactly what you are investigating and what you expect to find. It does not matter whether your hypotheses are true or false – you will still gain marks if your hypothesis turns out to be false. Your hypothesis should be clearly stated and testable. Brainstorm possible hypotheses for a task relating to the differences and similarities between boys and girls.

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Wf - 2003 Choosing the right sample Once you have decided your aims and set up a hypothesis then it is important to consider how you will test your hypothesis. To this end, there should be a discussion of what data is needed to test the hypothesis, how much and what type. Suggest the data that would be relevant to testing the following hypothesis: “In any particular age group, boys are taller than girls” Your sample size must be at least 30

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Wf - 2003 Sampling techniques include: Random sampling is where each member of the population has an equally likely chance of being selected. An easy way to do this would be to give each person a number and then choose the numbers randomly. Systematic sampling is the similar to random sampling except that there is some system involved such as numbering each person and then choosing every 20 th number to form the sample. Stratified sampling is where each person is placed into some particular group or category (stratum) and the sample size is proportional to the size of the group or category in the population as a whole. Convenience sampling or opportunity sampling is one which involves simply choosing the first person to come along … although this method is not particularly random!

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Wf - 2003 Imagine you are going to conduct a survey of the opinions of pupils at this school about school uniform. Describe how you would collect the following samples: a random sample a systematic sample a stratified sample a convenience sample You must be very careful to avoid any possibility of bias in your work. For example, in making comparisons it is important to ensure that you are comparing like with like. For example, a comparison between the number of graphics used in a newspaper and the number in a magazine must include some consideration of the relative sizes of the two publications – newspapers are larger than magazines.

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Wf - 2003 Methods and calculations You can represent the data using statistical calculations such as the mean, median, mode, range and standard deviation. E.g. Hypothesis being tested: “Students are better at estimating the length of a line than the weight of a package”. Tabulated calculations: Length(cm) Weight (g) Mean15.9105.2 Median15.5100 Mode 14100 Range 8.6 28 St Dev 1.2 2.1 Note: the actual length of the line is 15cm and the weight of the package is 100g. Using the table: What do you notice about the average of the length and weight? What do you notice about the spread of the length and weight? Does the information support the hypothesis? It is important to consider whether information on all of these statistical calculations is essential.

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Wf - 2003 Points to note about the statistical calculations: The mean, mode and median are all measures of central tendency The range, inter-quartile range, (percentiles) and standard deviation are all measures of spread (variability). When comparing two distributions you should consider an average and a measure of spread. Choose the best representative value for you data (e.g. the median). Do not be repetitive. Ensure a good range of appropriate techniques, including some higher tier techniques if appropriate. GCSE Stats students should try to include calculations such as standard deviation (measure of spread) and Spearman’s Rank Correlation (measures the strength of correlation between two variables).

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Wf - 2003 Graphical representation It may be useful to show your results using graphs and diagrams as sometimes it is easier to see trends. Graphical representation might include: Pie charts, bar charts, scatter diagrams, stem and leaf diagrams, histograms, cumulative frequency graphs and box-whisker diagrams. Moderator comment: You should only use appropriate diagrams and graphs. Remember: you should comment on why you are choosing to include a particular diagram and, after you have drawn it, what inferences you can make based on the diagram.

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Wf - 2003 Matching the graph to the purpose of the investigation The four main reasons for collecting data are: Describing Summarising Here are a few examples to give you an idea of what is meant above. PurposeTypical statements DescribingThere are 14 boys and 15 girls The tallest person in the class is a girl SummarisingThe modal class height is 1.50-1.55m The heights of Paul and Tom are typical of the class ComparingThere are more boys than girls There are more tall girls than tall boys GeneralisingGirls seem to be taller than boys at this age Comparing Generalising

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Wf - 2003 This table shows you which diagrams and calculations fit each purpose: Types of data Purposes DescribingSummarisingComparingGeneralsising CategoriesBar chart Pie chart Bar charts Pie charts Discrete variable Bar chart Pie chart Stem plot Mean, mode Median Range Bar charts Pie charts B-B stem plots Continuous variable Stem plot Histogram Mean, mode Median Range B-B stem plots Histograms Bivariate (discrete or continuous) ScatterplotLine of fit

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Wf - 2003 Summarising and interpreting the data You should refer to your original hypothesis when you summarise your results. Moderator comment: In your conclusion you should also suggest limitations to your investigation and explain how these might be overcome. You may wish to discuss: sample size sampling methods biased data other difficulties Hint: You need to appreciate that the data is more secure if the sample size is 500 rather than 50.

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Wf - 2003 Extending the task In your extension you should: Give a clear hypothesis Collect further data if necessary Present your findings using charts and diagrams as appropriate Summarise your findings referring to your hypothesis To gain better marks in your coursework you should extend the task in light of your findings.

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Wf - 2003 Using a computer Whether you have computer-generated or hand-drawn tables and diagrams you should check the following: The tables are clear The diagrams are labelled clearly The diagrams have titles There is a wide variety of diagrams They are all appropriate Remember there is no need to use every type The calculations are clearly written out They are appropriate and relevant It is quite acceptable that calculations and representations are generated by computer, as long as any such work is accompanied by some analysis and interpretation. Accuracy check

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Wf - 2003 This list of statistics is often useful in investigative tasks: Calculating averages (mean, mode and median) Finding the range Pie charts, bar charts, stem and leaf diagrams Constructing a cumulative frequency graphs Finding the inter-quartile range Histograms Calculating the standard deviation Drawing a scatter graph and line of best fit Sampling techniques Discussing bias In this presentation I have tried to give you some hints on approaching statistical coursework to gain the best possible mark. Remember: None of these will gain you marks if they are not appropriate and relevant to your enquiry!

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© Boardworks Ltd 2005 1 of 40 D5 Frequency diagrams for continuous data KS4 Mathematics.

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