A1-D-1-1

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A1.D.1.1 Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics.

In a Nutshell

Students will be able to communicate fluently about data sets using various displays and measures of central tendency, showing a deep understanding of the various summary statistics.

Student Actions	Teacher Actions
Students will analyze data in different displays including tables, scatter plots, stem and leaf plots and box and whisker plots and develop a deep and flexible conceptual understanding of the meanings of measures of central tendency in context. Students will calculate mean, median, mode, range and all quartiles of the data with accurate and appropriate procedural fluency. Students Develop a productive mathematical disposition as they make sense of data sets and their meanings in context. Students use various representations to share data sets with others and communicate mathematically the meanings of the measures of central tendency for those data sets to show understanding.	Implement tasks that promote reasoning and problem solving that include data sets and graphs which represent real-world problems. Pose purposeful questions, asking students to not only find measures of central tendency but also to interpret their findings accurately. Elicit and use evidence of student thinking as students justify their processes and explain their interpretations of solutions of data analysis in context to real world situations.
Key Understandings	Misconceptions
Students will be able to compute: mean, median, mode, and range. Students will be able to create scatter plots, box and whisker plots, and stem and leaf plots. Students will be able to choose the most appropriate representation of data and the most appropriate measure of central tendency for various situations. Students will correctly interpret the meanings of various measures of central tendency in context. Example: Students in biology earned the following scores on their exam. 87, 95, 100, 76, 65, 97, 62, 88 Find the mean, median, mode and range for the data. Display the data in: Scatterplot Stem and leaf plot Box and whisker plot c. The teacher has promised the students a reward if the class average is an 85%. One student has not tested yet; what score must he earn to raise the class average to 85%? Solution: 83.75, 87.5, none, 38 respectively (desmos.com-https://www.desmos.com/calculator/fzudneekir) Sample size: 8 Median: 87.5 Minimum: 62 Maximum: 100 First quartile: 67.75 Third quartile: 96.5 Interquartile Range: 28.75 Outliers: none (http://www.alcula.com/calculators/statistics/box-plot/) c. 670 + x 9=85 670+x=765 x=95 The student must earn a 95% to raise the class average to 85%.	Students fail to put numbers in order before finding median. Students misunderstand the meanings of the quartiles in box and whisker plots.