MA4-20SP Single Variable Data Analysis.docx



MA4-20SP Single Variable Data Analysis Summary of Sub StrandsDurationMA4 – 19SP Data Collection and RepresentationDuration: 3 weeksStart Date:Completion Date:Teacher and Class:Unit overviewOutcomesBig Ideas/Guiding QuestionsThis unit focuses on analysing data of a single variable. Students should be introduced to this terminology and be given many opportunities to apply statistics to everyday situations. Students need to discuss what information can be drawn from the data presented and communicate these ideas and information. The analysis of data will involve the calculation of mean, mode, median and range.MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbolsMA4-2WM applies appropriate mathematical techniques to solve problemsMA4-3WM recognises and explains mathematical relationships using reasoningMA4-20SP analyses single sets of data using measures of location, and rangeThis substrand provides many opportunities to communicate ideas and information. This could be done as a project and be done collaboratively with other students or even across KLAs. This is also a good time to use technology including spreadsheets to present this data, graphically and/or in a table and then to analyse the data using spreadsheet functions. Key WordsData, collect, organise, display, analyse, graphical, table, frequency distribution table, mean, average, , sum, mode, median, range, statistical functions, context, appropriate, measures of location, centre and spread, outlier, effects, clusters, gaps, errors, justify, describe, interpret, frequency histograms, stem-and-leaf plots, dot plots, conclusions, variables, variation, random samples, explain, observation, investigate, census, compare, recognize, suggest, prefer, better, best, other superlatives and comparatives such as safer, healthier, taller, etc.Catholic PerspectivesSchool Free Design The Mathematics teachers undertake to uphold the ethos and teachings of the Catholic church and to support the liturgical life of the College. They promote in the classroom a sense of compassion, respect between students and staff and a positive and supportive learning environment.Students can look at truth and honesty in displaying and analyzing data and what is reported in the media. For example, often the report in the newspaper or on a website, will state that the average property price is a certain value when they are really giving you the median. Why?Assessment OverviewThis topic can be done using a project such as the one on the Census At School website: Are Male Drivers Better than Female? is also a skateboard survey that students could do and hand in a report about their findings. , learning and assessment Resources Stage 4 - Single Variable Data AnalysisStudents:Calculate mean, median,?mode and?range for sets of?data and interpret these statistics in the context of data (ACMSP171)calculate the mean, , of a set of data using recognise that the mean is often referred to as the 'average' in everyday language (Communicating)use the statistical functions of a calculator to determine the mean for small sets of data (Problem Solving) use the statistical functions of a spreadsheet to determine the mean for large sets of data (Problem Solving) determine the median, mode and range for sets of datarecognise which statistical measures are appropriate for the data type, eg?the mean, median and range are meaningless for?categorical data (Reasoning) use the statistical functions of a spreadsheet to determine the median, mode and range for large sets of data (Communicating, Problem Solving) identify and describe the mean, median and mode as 'measures of location' or 'measures of centre', and the range as a 'measure of spread' describe, in practical terms, the meaning of the mean, median, mode and/or range in the context of the data, eg?when referring to the mode of shoe-size data: 'The most popular shoe size is size 7' Investigate the effect of individual data values, including outliers, on the mean and median (ACMSP207)identify any clusters, gaps and outliers in sets of data investigate the effect of outliers on the mean, median, mode and range by considering a small set of data and calculating each measure, with and without the inclusion of an outlier explain why it is more appropriate to use the median than the mean when the data contains one or more outliers (Communicating, Reasoning) determine situations when it is more appropriate to use the?median?or?mode, rather than the mean, when analysing data, eg?median for property prices, mode for shoe sizes (Reasoning) analyse collected data to identify any obvious errors and justify the inclusion of any individual data values that differ markedly from the rest of the data collected Describe and interpret?data displays using mean, median and range (ACMSP172)calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including?frequency distribution tables, frequency histograms,?stem-and-leaf plots and dot plots draw conclusions based on the analysis of data displays using the mean, median and/or mode, and range Explore the variation of means and proportions of random?samples drawn from the same population (ACMSP293)investigate ways in which different random samples may be drawn from the same population, eg?random samples from a?census may be chosen by gender, postcode, state, etccalculate and compare summary statistics (mean, median, mode and range) of at least three different random samples drawn from the same populationuse a spreadsheet to calculate and compare summary statistics of different random samples drawn from the same population (Communicating, Problem Solving) recognise that summary statistics may vary from sample to sample (Communicating)recognise that the way in which random samples are chosen may result in significant differences between their respective summary statistics, eg?a random sample of girls compared to a random sample of boys from the population, random samples chosen by postcode (Communicating, Reasoning) suggest reasons why different random samples drawn from the same population may have different summary statistics (Communicating, Reasoning) Define each of the measures of location, that is, the mean, median and mode. There is a song on you tube that you could play to help students remember it.Calculate the average of a set of scores. Could use examples from sport, etc. Introduce how to calculate the mean using the formulaShow students how to use their calculator to determine the mean for small sets of data. Make sure that students all have the same calculator as the statistical functions differ greatly on each calculator.Covered in next dot pointCollect some categorical data, such as type of car (colour or make), favourite sport (limit their choices) and then ask students to calculate the mean, median and range for this data. Ask students to explain why they cannot – what kind of data is this? Use the Census At School website and the activity: Calculating the mean, median and mode using Excel to cover this outcome.Describe the mean, median and mode as ‘measures of location’ or ‘measures of centre’ and the range as a ‘measure of spread.’Students are asked to describe given sentences Eg. Instead of staying that the mode of the colour of cars is white, they say The most common or most popular colour for cars is white. Instead of saying that the age range is 32, they should say that the ages of people at a concert was from 18 to 50, etc.Define what are clusters, gaps and outliers in the context of data. This could be done using a Maths Dictionary. Brainstorm and students write definitions in their OWN words.Collect data, such as height of students in the class or shoe size of students in the class. From this data, see if there are any clusters, gaps and outliers.Calculate the mean, median, mode and range of this data, with and without outliers. Students consider What effect does the inclusion of the outlier have on each of the measures of location and spread? Should we include any outliers?Should we use the mean or median in this case?Give scenarios, for example, wages or property prices and students are asked which they would use in each case, for example, the median or mode, rather than the mean would be more appropriate in some situations. They are to justify their choices using the mathematics involved.Students could then use the given website from Census At School. It allows students to change various values and to see the effect that these have on the measures of location and spread.Also, there is an activity on belly button height. It tells you which ones to be considered as outliers and students are asked to explain their working as they go. (Part of this could be an extension as not all students will be able to do this activity in full)Show students how to calculate the mean, median, mode and range for data represented in a variety of ways.There is a video tutorial on stem-and-leaf plots that could be helpful for someUse of the Random Sampler from the Census At School Website.Talk about ways I might choose different random samples from the school population eg. Gender, Age, Residence, etc. Use the class as an example and collect information such as the four measurements in the Who Am I website?, that is, height, arm length, foot span and height of belly button from floor when standing. Then compare the data you have collected with others in the class. Represent your finding using statistics and compare and contrast your findings to that of others.They need to consider:Do the summary statistics change or not? Why?When was there the biggest difference between two sets of statistics? Why are there differences statistics when you draw the information from the same population? There is a set of tutorials on this including a student resource and a teacher resource. It has an interactive activity for the students for them to gain an understanding of this content. For the mean, median and mode song: the mean, median and mode using Excel: are some tutorials on the Census At School Website that may be helpful to some students: the Census At School Australia website : on random sampling and variations in samples: Class: __________________________Start Date: _______________________Finish Date: ______________________Teacher’s Signature: _______________________Teachers evaluate the extent to which the planning of the unit has remained focused on the syllabus outcomes. After the unit has been implemented, there should be opportunity for both teachers and students to reflect on and evaluate the degree to which students have progressed as a result of their experiences, and what should be done next to assist them in their learning.Evaluation reflects:The effectiveness of the program in meeting the diverse needs of students and identifies curriculum adjustmentsLevel to which syllabus outcomes have been demonstrated by studentsThe effectiveness of pedagogical practices employedSuggested program adjustmentsElements of the school’s Contemporary Learning FrameworkSample questionsHighlight the response that best describes your view to the following statements and provide comments in the spaces provided.The set text/s (if relevant) were suitable for the student needs and interests:STRONGLY AGREEAGREEUNSURESTRONGLY DISAGREEThere were sufficient and suitable resources to teach the unit:STRONGLY AGREEAGREEUNSURESTRONGLY DISAGREEThere was sufficient time to teach the set content:STRONGLY AGREEAGREEUNSURESTRONGLY DISAGREEAssess the degree to which syllabus outcomes have been demonstrated by students in this unit:............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Evaluate the degree to which the diverse needs of learners have been addressed in this unit:............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Comment on the effectiveness of pedagogical practices employed in this unit:........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Assessment was meaningful and appropriate to reflect student learning and achievement:............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Suggested program adjustments / other comments:............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ................
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