STATISTICS AND PROBABILITY: DATA ANALYSIS Grade 2–12 General Outcome: Collect, display, and analyze data to solve problems. Goran, Wendy, Grace, Joshua 1

Grades 2 and 3 Gather and record data about self and others to answer questions Organize data using objects, tallies, check marks or lists. Construct and interpret concrete pictographs and graphs (bar graphs start in gr.3) 2 2

Grades 4 and 5 One-to-one and many-to-one correspondence graphs Differentiate between first-hand and second- hand data Double bar graphs attributes (title, axes, intervals, and legend) 3 3

Grade 6 Line graphs and double graphs: Create from data, interpret, and draw conclusions Sample question: In 2002, did New Hamburg or Briggs Corner have fewer home sales? 4 4

Grade 6 Select methods of collecting data (questionnaires, experiments, databases, electronic media…) Graph data and analyze graphs to solve problems Draw histograms Sample question: How many people waited between 51 and 61 minutes? 5 5

Grade 7 Measures of range and central tendency (mean, median, mode) Determine for given set of data Effect of outliers Sample question: What is the median number of houses in each town? 6 6

Grade 7 Construct, label, and interpret circle graphs: Translate graph angle quantities into percentages Stem-and-leaf plots 7 7

Grade 8 Critique and compare ways data is presented Same data presented by different types of graphs: circle graphs, line graphs, bar graphs, double bar graphs, and pictographs Advantages and disadvantages of different graphs for presenting specific set of data Sample Q: Would you use a bar graph, pictograph, double bar graph, or circle graph to show number of boys and girls per grade? 8 8

Grade 8 Misconceptions/misinterpretations from graph formatting Conclusions about inconsistency with a given data set or graph, and the misinterpretation 9 9

Grade 9 Describe factors that affect data collection: bias, language, ethics, cost, time and timing, privacy, cultural sensitivity Sample Question: Sofie read 7 randomly chosen books from each library in her city. Each library is the same size. Is this sample of the city's books likely to be biased? 10

Grade 9 Describe factors that affect data collection: Bias, language, time and timing… Select and defend the choice of using either a population (census) or a sample of a population (sample) to answer a question Understand and choose an appropriate sample: Simple random sampling, cluster sampling… Sample Question: Winnipeg’s city council wants to find out if its residents are satisfied with the garbage removal service. Should a sample or census be used to collect the data? Explain why. 11

Grade 9 Develop and implement a project plan for the collection, display, and analysis of data (1) Prepare a question. (2) Identify the population and choose a sample. (3) Collect the data. (4) Analyze and display the data. (5) Evaluate your plan. Sample Question: Design a survey to find out the favourite radio station of students in your school. 12

Grade 10 No data analysis in Grade 10 Foundation Pre-Calculus A & W 13

Foundation of Mathematics 11 Normal distribution, including: standard deviation (σ) z-scores. 14

Foundation of Mathematics 11 Standard Deviation (σ): (how much variation or "dispersion" ) 15

Foundation of Mathematics 11 Sample question: The mean height of the high school basketball players is 181 cm, and the standard deviation is 6 cm. What percent of players is between 169 cm and 175 cm? 16

Foundation of Mathematics 11 Z-scores : Standard scores population mean raw score to be standardized Students learn how to calculate the x scores and standard deviation 17 17

Foundation of mathematics 11 Z-score table How to use x-score table 18 18

Foundation of Mathematics 11 They also learn how to use TI84 for statistics. 19

Foundation of Mathematics 11 Students can interpret statistical data, using: confidence intervals confidence levels margin of error. 20

Creating and Interpreting Graphs A & W Maths 11 Creating and Interpreting Graphs Histograms Bar Graphs Line Graphs Circle Graphs Sample problem: If there are 150 restaurant accidents per year in Kelowna, how many of them would you expect to be burns and scalds? Determine which advantages/disadvantages of different graphs for given data set. Explain how different graphs explain different aspects Create graph from data (with/without technology) Describe graph trends Interpolate/extrapolate values from graph Solve contextual problems from graph.

Creating and Interpreting Graphs A & W Maths 11 Creating and Interpreting Graphs Histograms Bar Graphs Line Graphs Circle Graphs Connection: Also working with linear equations this year

Analysing Central Tendency A & W Maths 12 Analysing Central Tendency Mean Median Mode Weighted Mean Advantages/disadvantages of the different measures. Working with outliers. (trimmed mean, effect on mean, etc.) Identify/correct errors in calculations of central tendency. Work with percentiles. Contextual problems Trimmed Mean Percentiles

weighted mean, percentiles… Overview of Pathways collecting data Gr. 6–7 mean… Gr. 8 vs Gr. 9 sampling Gr. 10 AW11: no data analysis since Gr 9, but no big jump in difficulty. AW12: AW11 builds on Gr 8 topic, but AW12 builds on Gr 7 topic σ, z-score… Gr. 11 weighted mean, percentiles… Gr. 12 A & W Foundations 24

Remediation for HUGE hole in Grade 10 Teach quartiles, inter-quartile range in Grade 10

Remediation for HUGE hole in Grade 10

weighted mean, percentiles… Overview of Pathways collecting data Gr. 6–7 mean… Gr. 8 vs Gr. 9 sampling Gr. 10 Overall, pretty happy with the progression of data analysis, except for the hole in Grade 10. Grace offered remediation. Another minor problem? Central tendency is not integrated into other topics: Grade 7, it’s taught alongside circle graphs Grade 12, it’s a standalone unit, not taught with graphing Therefore, maybe swap out Gr 7 circle graphs for histograms Could close grade 12 with an data analysis project that ties everything together, like the one in Gr 9 σ, z-score… Gr. 11 weighted mean, percentiles… Gr. 12 A & W Foundations 27