ࡱ>  bjbjVV ;^<<X0U 8#TwJ\#9999/>>/R/ [[[[[[[$:^`h[^/.^/^/^/[99i\111^/<99[1^/[11X[|Q[9+0pY"[\0J\YDa0|DaDQ[DaQ[d^/^/1^/^/^/^/^/[[1^/^/^/J\^/^/^/^/Da^/^/^/^/^/^/^/^/^/ : Title: A Tall Tale Achievement Objectives: S5-1B Considering sources of variation S5-1D Using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets S5-1E Comparing sample distributions visually, using measures of centre, spread, and proportion Key Competencies: Thinking: Seek patterns and generalisations Relating to Others: Share ideas Using Language, Symbols & Texts: Interpret visual representations This activity covers the following key ideas: key words are in bold It explores the effect of sample size on the distribution of a sample (sample distribution) It explores how samples of the same size vary It explores how samples of different size vary It explores the connection between the distribution of a population (population distribution) and the distribution of a sample (sample distribution) Resources OHTs of pre-test graph OHTs of several cards of same size Teacher access to computer Worksheets for students Prior Knowledge: Construct dot plots and identify key features of centre, spread and shape Understand keywords population and sample Definition of distribution: A statistical distribution shows how often the values of what is being measured (the variable) occur (their observed frequency). Write I notice statement (should have already done a bit of work on constructing and analysing dot plots) about dot plots using statistical language such as majority, outliers, spread, skew, average Adapting for ICT Introduction/Background This activity focuses on growing samples and looking at the effect on the distribution of values. The previous lessons ideas on sample, population, sample distribution, population distribution will also be reinforced. Students will be asked to predict the distribution of data values for various sample sizes. These are then compared to actual samples taken from the CensusAtSchool website. This will lead to a discussion of what the students think the height distribution for all Year 10 new Zealand girls looks like. Types of shapes for distributions:  Problem What would a graph of the heights of Year 10 NZ girls look like? What stories do distributions of samples tell? Samples of same size Cycle 1 Samples of different sizes Cycle 2Samples compared to population Cycle 3Plan Teacher says: Predict a graph of the heights of 10 year 10 girls. Lets compare this with the graph of the heights of ten real students. (Use real data from the class or census at school). Are they different from your own predictions? Describe the differences. You can use words such as majority, outliers, spread, average.Teacher says: We will now have a look at how the graph changes for larger samples. Predict a graph of the heights of one class (27 students) of year 10 girls. Lets compare this with the graph of the heights of 27 real students. (Use real data from the class or census at school). Are they different from your own predictions? Describe the differences. Repeat this process for heights of 3 classes (about 90 students). Teacher says: Predict a height graph of all Year 10 girls. You do not need to draw dots. It is the shape of the graph that is important. Teacher could sketch possible shapes on the board. Class discuss which is the best shape, perhaps by elimination, giving reasons. Generate dot plot of all relevant data from census at school. Data Analysis  For samples of a given size, discuss and compare the shape of the distributions the centre (where the middle value is) of the distributions the spread of the distributions For samples of different size discuss and compare the shape / centre /spread Discuss and compare how the sample distributions compare with the population distribution. Emphasise: (1) that for a given sample size each sample is different (2) that as the sample size increases the graphs/distributions of the samples of the same size look more alike (3) that as the sample size increases the sample distribution gets closer to the distribution of the population distribution Encourage students to use statistical language when they describe the graphs. Write key words (sample, population, sample distribution, population distribution, majority, outliers, spread, skew, symmetry and average) on the board for students to refer to. To encourage more discussion about the shape of the population graph show the following sketches of graph shapes.  Conclusion Summarize the findings. For example, the teacher could pose these questions: What do you notice about the average and spread of the sample distributions when the sample size is small? What do you notice about the average and spread of the sample distributions as the sample size gets bigger? What do you notice about the average and spread of the sample distributions when the sample size is very large? If you have a large enough sample, what can you say about the population? Reflection Each sample is different from all others there is variability between samples of the same size. As the sample size increases the graphs of the samples become more alike. What is the relationship between the distribution of the sample for a given sample size and the population distribution? What do you notice about the average and spread?What do you notice about the average and spread?What do you notice about the average and spread? To extend this activityHow would the graph for all Year 10 students be different to the graph of female students? How would the graph for boy students be different to the graph for girl students? Predict centre of population based on samples.  This activity is based on: Bakker, A. 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