Activity 2: Comparing Distributions
Activity
In this activity, students will use a graphing calculator (TI-83/84 Plus is recommended) to make graphical displays of quantitative data. The graphing calculator will be used primarily to create and compare boxplots for the two sets of data from the beginning of the unit plan.
Students will then use a web-based applet to explore dotplots and histograms, as well as create boxplots again. The applet allows students to use automatically generated data or copy and paste data from another problem. Students will use the applet to explore the affects of extreme values on measures of center and spread. The graphical displays will help students visualize the different shapes of distributions and how the mean and the median compare for symmetric and skewed distributions.
Prerequisite Knowledge
Rationale
Through the use of the graphing calculator and applet, students are able to persevere through the problem addressed at the beginning of the unit. Students must use the technology to create graphical displays (dotplots, histograms, and boxplots) to visualize distributions of the data in order to make quantitative comparisons. Students will use quantitative data and technology to make arguments and inferences about the data presented at the beginning of the unit by comparing measures of center (median and mean) and spread (interquartile range and standard deviation). Students must use the appropriate technology and be very precise in using the technology in order to make predictions and viable arguments about the differences in shape, center, and spread of a distribution that contains outliers.
CCGPS Standards Addressed
Mathematical Practice Standards Addressed
In this activity, students will use a graphing calculator (TI-83/84 Plus is recommended) to make graphical displays of quantitative data. The graphing calculator will be used primarily to create and compare boxplots for the two sets of data from the beginning of the unit plan.
Students will then use a web-based applet to explore dotplots and histograms, as well as create boxplots again. The applet allows students to use automatically generated data or copy and paste data from another problem. Students will use the applet to explore the affects of extreme values on measures of center and spread. The graphical displays will help students visualize the different shapes of distributions and how the mean and the median compare for symmetric and skewed distributions.
Prerequisite Knowledge
- Students should know how to calculate descriptive statistics (measures of center and spread) prior to this activity
- Students should know that boxplots, dotplots, and histograms are used to show the distribution of a quantitative variable
Rationale
Through the use of the graphing calculator and applet, students are able to persevere through the problem addressed at the beginning of the unit. Students must use the technology to create graphical displays (dotplots, histograms, and boxplots) to visualize distributions of the data in order to make quantitative comparisons. Students will use quantitative data and technology to make arguments and inferences about the data presented at the beginning of the unit by comparing measures of center (median and mean) and spread (interquartile range and standard deviation). Students must use the appropriate technology and be very precise in using the technology in order to make predictions and viable arguments about the differences in shape, center, and spread of a distribution that contains outliers.
CCGPS Standards Addressed
- Summarize numerical data sets in relation to their context (MCC6.SP.5)
- Represent data with plots on the real number line (dot plots, histograms, and box plots) (MCC6.SP.4, MCC9-12.S.ID.1)
- 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. (MCC6.SP.2, MCC6.SP.5, MCC9-12.S.ID.2)
- Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers) (MCC9-12.S.ID.2, MCC9-12.S.ID.3)
Mathematical Practice Standards Addressed
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Use appropriate tools strategically.
- Attend to precision.