ࡱ> +-()* ?bjbjBrBr   3rr )!)!)!4]!]!]!h!i" ]!Ec(u##C$C$C$-vC.$g.bbbbbbbmehb)!{.-"-{.{.b C$C$h b+3+3+3{. RC$)!C$b+3{.b+3+3[!"`C$:N]!E/d]4b c<Ec$^t+i/+ih``8+i)!`{.{.+3{.{.{.{.{.bb+3{.{.{.Ec{.{.{.{.+i{.{.{.{.{.{.{.{.{.r {:  Internal Assessment Resource Mathematics and Statistics Level 3 This resource supports assessment against: Achievement Standard 91581 Investigate bivariate measurement dataResource title: Sport science4 creditsThis resource: Clarifies the requirements of the standard Supports good assessment practice Should be subjected to the schools usual assessment quality assurance process Should be modified to make the context relevant to students in their school environment and ensure that submitted evidence is authentic Date version published by Ministry of EducationDecember 2012 To support internal assessment from 2013Quality assurance statusThese materials have been quality assured by NZQA. NZQA Approved number A-A-12-2012-91581-01-6203Authenticity of evidenceTeachers must manage authenticity for any assessment from a public source, because students may have access to the assessment schedule or student exemplar material. Using this assessment resource without modification may mean that students work is not authentic. The teacher may need to change figures, measurements or data sources or set a different context or topic to be investigated or a different text to read or perform. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91581: Investigate bivariate measurement data Resource reference: Mathematics and Statistics 3.9A Resource title: Sport science Credits: 4 Teacher guidelines The following guidelines are supplied to enable teachers to carry out valid and consistent assessment using this internal assessment resource. Teachers need to be very familiar with the outcome being assessed by Achievement Standard Mathematics and Statistics 91581. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it. Context/setting This activity requires students to investigate relationships between physical and/or physiological attributes of a sample of high performance athletes from the Australian Institute of Sport. Students will need to understand the given variables. Class time should be set aside for this purpose before the assessment. This activity can be adapted to use another existing data set. Any data set provided needs to have appropriate motivation, contextual depth and relevance to the students. Details about the data need to be provided to enable students to inform themselves about the context. Conditions This activity requires multiple sessions to complete an investigation. Confirm the timeframe with your students. Students will present their work and findings independently. The students need to use appropriate technology, for example, statistical software. The format of the presentation could be, but is not restricted to, a written report. Resource requirements The data set referred to for this assessment is available from  HYPERLINK "http://www.statsci.org/data/oz/ais.html%20" http://www.statsci.org/data/oz/ais.html This data set should be made available as a spreadsheet for students to use for the assessment. Additional information None. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91581: Investigate bivariate measurement data Resource reference: Mathematics and Statistics 3.9A Resource title: Sport science Credits: 4 Achievement Achievement with Merit Achievement with ExcellenceInvestigate bivariate measurement data.Investigate bivariate measurement data, with justification.Investigate bivariate measurement data, with statistical insight. Student instructions Introduction Sports scientists use statistical information to understand how different variables are related. This activity requires you to carry out a bivariate data investigation using at least two variables and to write a report of your findings. Your overall grade will be determined by how well you carry out your investigation and how well you apply the statistical enquiry cycle. You will work independently over a period of <> to complete this task. Task The relationship between different variables and the performance of the athlete is an area of investigation for those interested in training athletes. You have been given data from athletes collected at the Australian Institute of Sport. (See Resource A for column heading descriptors.) Use the statistical enquiry cycle to carry out a statistical investigation to determine if there is a relationship between at least one pair of variables. Write a report describing the investigation. Familiarise yourself with the data set provided. This will include doing research to help you understand the variables and develop a purpose for the investigation. Pose an appropriate relationship question that can be answered using variables in the data set. The variables you choose must be numerical, and the variable you use as your response variable must be continuous. You may choose to investigate more than one pair of variables. Select appropriate display(s) to graph your data. Identify features in the data, including the nature and strength of the relationship. Find an appropriate model. Use your model to make prediction(s). Write a conclusion answering your question. Support your conclusion by referring to your analysis and/or features of the visual display(s). Include a reflection on your process, which could consider other relevant variables, or evaluate the adequacy of your model(s). In writing your report, link your discussion to the context and support the statements you make by referring to statistical evidence. Resource A The data set provides information about 102 male athletes and 100 female athletes at the Australian Institute of Sport. Explanation of column headers in the data set: Sexmale or femaleSportsport playedHtheight in cmWtweight in kgLBMlean body mass in kg%Bfat% body fatBMIbody mass index (weight/height2)RCCred blood cell countWCCwhite blood cell countHchaematocritHghaemoglobinFerrplasma ferritin concentrationSSFsum of skin folds Assessment schedule: Mathematics and Statistics 91581 Sport science Teachers note: You will need to adapt this assessment schedule to include examples of the types of responses that can be expected. Evidence/Judgements for Achievement Evidence/Judgements for Achievement with MeritEvidence/Judgements for Achievement with ExcellenceThe student investigated bivariate measurement data. They have shown evidence of using each component of the statistical enquiry cycle. The student has: posed an appropriate relationship question selected and used appropriate display(s): For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship: For example, stated from a visual inspection that the trend is linear rather than non-linear. They have described the strength with reference to visual aspects of scatter about the regression line and the nature, in context, by stating that as one variable increases the other also tends to increase. Other features and unusual points have been identified. found an appropriate model: For example, fitted an appropriate regression model to the data. made a prediction: For example, used the model to make a prediction for the response variable. The prediction is sensible with respect to the context and uses units and sensible rounding. communicated findings in a conclusion: For example, clearly communicated each component of the cycle. They have made a conclusion which is consistent with their question. The examples above are indicative of the evidence that is required The student investigated bivariate measurement data, with justification. They have shown evidence linked components of the statistical enquiry cycle to the context and made supporting statements by referring to evidence such as statistics, data values, trends, or features of visual displays. The student has: posed an appropriate relationship question. selected and used appropriate display(s): For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship: For example, stated from a visual inspection, with evidence, that the trend is linear rather non-linear. They have described the strength with references to visual aspects of the scatter about the regression line. They have described, in context, the nature by stating as one variable increases the other also tends to increase and justified this with reference to visual aspects of the display(s). They have included consideration of possible contextual reasons for the features. They may have acknowledged that they have found only a statistical relationship between the variables but that this does not imply causation. found an appropriate model: For example, fitted an appropriate regression model to the data. The appropriateness of the model is justified by discussion of fit throughout the range of x-values in the data or the number of data points. made a prediction: For example, used the model to make a prediction for the response variable. The prediction is interpreted in context with the use of units and sensible rounding. It is justified with discussion on how precise it might be and has supported comments with references to statistical evidence from the analysis. communicated findings in a conclusion: For example, clearly communicated each component of the cycle. There is contextual support for the conclusion which is consistent with their question. They may have considered, giving contextual reasons, the possibility of investigating their chosen relationship separately for males and females. The examples above are indicative of the evidence that is required. The student has investigated bivariate measurement data, with statistical insight. They have shown evidence of integrating statistical and contextual knowledge throughout the process. They may have reflected on the process, considered other relevant variables, or evaluated the adequacy of any models. The student has: posed an appropriate relationship question selected and used appropriate display(s) For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship For example, stated, with evidence, that the trend is linear/non-linear. They have described the strength with references to visual aspects of the scatter about the regression line. They have described, in context, the nature by stating that as one variable increases the other also tends to increase and justified this with reference to visual aspects of the display(s). Other features of the data have been discussed with supporting comments. They have reflected on the strength and nature of the relationship with contextual comments. They may have acknowledged that they have found only a statistical relationship between the variables but that this does not imply causation. They may have acknowledged that other factors (named) would impact on the variable. They have reflected on features by discussing their relevance to a wider population. found an appropriate model For example, fitted an appropriate regression model to the data. The appropriateness of the model is justified by discussion of fit throughout the range of x-values in the data. Consideration has been given to aspects such as the number of data points. They may have considered improvements to the model by considering other models that might be more appropriate. They may have extended the investigation by developing models with data that has been separated into relevant subsets. made a prediction For example, used the model to make a prediction for the response variable. The prediction is interpreted in context with the use of units and sensible rounding. It is justified with discussion on how precise it might be and is supported by comments with references to statistical evidence from the analysis. They may have justified the choice of variable to use for predictions by giving reasons for using the selected one rather than others. They have reflected on predictions by discussing their relevance to a wider population. The prediction may have been made using alternative models and the accuracy of these has been discussed in the context of the investigation. Communicated findings in a conclusion: For example, clearly communicated each component of the cycle. They have extended their initial investigation (for example, investigating males and females separately), giving contextual reasons to justify the extension and discussing the results of the extended investigation with respect to their question. The examples above are indicative of the evidence that is required. Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard.     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