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Regular Statistics Unit 2: Displaying and Interpreting Univariate Data Enduring understanding (Big Idea): Students will understand that data analysis involves describing data using graphs and numerical summaries which helps us see and understand the most important features of a set of data. Essential Questions: 1. What type of graph would be best used with this data? 2. What can be concluded from this graph? 3. What is the five number summary for this data? BY THE END OF THIS UNIT: Students will know… how to create a variety of graphs to represent data and how to choose the best one how to calculate single variable statistics. Vocabulary: (in the order they appear) Distribution, Pie Chart, Bar Graph, Dotplot, Stemplot, Histogram, Overall Pattern, Deviations, Outliers, Shape, Center, Spread, Symmetric, Skewed, Five-Number Summary, Mean, Standard Deviation, Median, Interquartile Range, Boxplot, Line Graph, Trend, Seasonal Variation, Pictograms Unit Resources www.onlinestatbook.com (II. Graphing Distributions, III. Summarizing Distributions) http://www.learner.org/resources/series65.html (2. Picturing Distributions, 3. Describing Distributions) Decisions Through Data (Unit 2: Stemplots, Unit 3: Histograms and Distributions, Unit 4: Measures of Center, Unit 5: Box Plots, Unit 6: The Standard Deviation) Students will be able to… Create a pie chart, bar graph, line graph, dotplot, and stemplot. Look for the overall pattern of a dotplot and stemplot and for major deviations from the pattern. Create a histogram Look for the overall pattern of a histogram and for major deviations from the pattern. Assess from a dotplot, stemplot, or histogram whether the shape of a distribution is roughly symmetric, distinctly skewed, or neither. Find the five-number summary and draw a boxplot; use boxplots to compare distributions. Mathematical Practices in Focus: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated resoning Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data CORE CONTENT Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable Standard: S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots). Concepts and Skills to Master Graph numerical data on a real number line using dot plots, histograms, and box plots Describe and give a simple interpretation of a graphical representation of data Determine which type of data plot would be most appropriate for a specific situation SUPPORTS FOR TEACHERS Critical Background Knowledge Know how to compute a median Find the lower extreme (minimum), upper extreme (maximum), and quartiles Academic Vocabulary Dot plot, histogram, box plot, quartiles, lower extreme (minimum), upper extreme (maximum), median, outlier Suggested Instructional Strategies Resources The case studies at Textbook Correlation: http://www.onlinestatbook.com/2/case_studies/case.html Statistics Through Applications Gather or provide data and have students plot each Chapter 2 type of graph MARS Concept Development Lesson: (S.ID.1 through Analyze the strengths and weaknesses inherent in S.ID.4) each type of plot by comparing different plots of the Representing Data Using Frequency Graphs same data Have students collect their own data and choose a MARS Concept Development Lesson: (S.ID.1 through graph to represent it. S.ID.4) Representing Data Using Box Plots Data sets: http://www.freestatistics.info Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data Skill-based task The following data set shows the number of songs downloaded in one week by each student in Mrs. Jones’ class: 10, 20, 12, 14, 12, 27, 88, 2, 7, 30, 16, 16, 32, 15, 25, 15, 4, 0, 15, 6. Choose and create a plot to represent the data Problem Task On the midterm math exam, students had the following scores: 95, 45, 37, 82, 90, 100, 91, 78, 67, 84, 85, 85, 82, 91, 92, 93, 92, 73, 84, 100, 59, 92, 77, 68, 88. What are the strengths and weaknesses of presenting this data in a certain type of plot for: Students in a class? Parents? The school board? Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data CORE CONTENT Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable Standard: S-ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Concepts and Skills to Master Given two sets of data or two graphs, identify similarities and differences in shape, center and spread. Compare data sets and be able to summarize the similarities and differences between the shape, and measures of centers and spreads of the data sets. SUPPORTS FOR TEACHERS Critical Background Knowledge Know how to compute the mean, median, interquartile range, and standard deviation by hand in simple cases and using technology with larger data sets. Create a graphical representation of a data set Academic Vocabulary Mean, median, interquartiles range, standard deviation, center, spread, shape Suggested Instructional Strategies Resources The case studies at Textbook Correlation: http://www.onlinestatbook.com/2/case_studies/case.html Statistics Through Applications Chapter 2 Use technology to manipulate plots of dats sets to explore how changing data affects the measures of Data sets: http://www.freestatistics.info center and spread. Discuss what it means when related data sets have differing centers of spreads in relation to the context. Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data Sample Formative Assessment Tasks Skill-based task The boxplots show the distribution of scores on a district writing test in two fifth grade classes at a school. Compare the range and Medians of the scores from the two classes. Problem Task Plot data based on populations of European countries. Plot data based on populations of Asian countries. Compare and discuss differences in center and spread. Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data CORE CONTENT Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable Standard: S-ID.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Concepts and Skills to Master Given two sets of data or two graphs, identify similarities and differences in shape, center and spread. Interpret similaritieses and differences between the shape and measure of centers and spread of data sets. State the effects of any existing outliers. SUPPORTS FOR TEACHERS Critical Background Knowledge Know how to compute the mean, median, interquartiles range, and standard deviation by hand in simple cases and using technology with larger data sets. Create a graphical representation of a data set. Academic Vocabulary Extreme data point (outliers), skewed, center, spread Suggested Instructional Strategies Resources The case studies at Textbook Correlation: http://www.onlinestatbook.com/2/case_studies/case.html Statistics Through Applications Chapter 2 Use data from multiple sources to interpret differences in shape, center and spread Data sets: http://www.freestatistics.info Use data that includes outliers and explore what happens when outliers are removed. Discuss the effect of outliers on measures of center and spread and the effect on the shape Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes. Regular Statistics Unit 2: Displaying and Interpreting Univariate Data Sample Formative Assessment Tasks Skill-based task The boxplots show the distribution of scores on a district writing test in two fifth grade classes at a school. Which class performed better and why? Problem Task Find two similar data sets A and B (use textbook or internet resources). What changes would need to be made to data set A to make it look like the graph of set B? Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.