A B C D

Solutions for Session 10, Part D

See solutions for Problems: D1 | D2 | D3

Problem D1

 a. Gregory does not quantify his statement and may only be looking at the upper extreme value. The teacher could ask Greg to determine "how much taller" the boys are than the girls. b. Marie is comparing the variation in the data and notices overlap in the values. The teacher might ask her to quantify her response. c. Arketa is considering other representations that might make certain patterns and relationships between the data sets more apparent. The teacher could ask the class to consider additional ways to represent the data that would make some comparisons more visible. d. Michael correctly determines the median for each data set and quantifies "how much taller" the boys are than the girls by comparing the medians of the data sets. The teacher might ask the other students to react to Michael's statement and then consider why it can be useful to compare the medians of two data sets. e. Paul quantifies "how much taller" the boys are than the girls by comparing what he thinks are the medians of the data sets; what he found, though, was the middle of each range and not the middle of the data. This is an opportunity for the teacher to review the meaning of median as well as ways to find the median of a set of ordered data. f. Kassie believes that she is comparing the modes of the data sets, but when three or more values have the same number of data points, such as the boys, the data is considered not to have a mode. The teacher can review the meaning of mode and ask the students to speculate as to why statisticians say that a data set doesn't have a mode when three or more values have the same number of data points. g. DeJuan correctly calculates the means and quantifies "how much taller" the boys are than the girls by comparing the means of the data sets. The teacher could now have the students compare the medians and means of the two data sets. What does each tell us about the data? In this situation, is one comparison more appropriate than the other one? Why or why not? h. Carl is comparing intervals of the two data sets that contain the most data. The teacher could take this opportunity to focus further attention on the importance of examining intervals in considering how the data are spread out or bunched together.

Problem D2

 a. Arketa is comparing the variation by looking at the range of each data set. The teacher might ask her to quantify her response. b. Michael compares the data sets by looking at the medians. The teacher could ask Michael to point to the median on each box plot and then review that 50%, or half, of the data box plot is on each side of the median. c. Monique incorrectly reasons that one can further subdivide the lines (or boxes) and that a fractional part of a line reflects a fractional part of the data. The teacher should ask Monique how she arrived at those percentages and then show this same finding on the line pot to see if she recognizes the discrepancy. d. Gregory is correctly reasoning about the box plots with quartiles. The teacher might ask the rest of the class to evaluate Gregory's statement for its accuracy. e. Morgan is correctly reasoning about the spread of the middle 50% of the data on the box plots. The teacher might ask the rest of the class to evaluate the accuracy of Morgan's statement. f. Janet does not understand how the box represents quartiles of the data. The teacher could go back to the line plots of the data and actually draw the box plot directly over the data so that Janet can see the distribution of the data within the quartiles of the box plot.

Problem D3

 a. Kassie thinks that her class's sample is representative of the district if the district were defined as the population. The teacher could ask the other students to give reasons for supporting or refuting Kassie's conjecture. b. Nichole uses personal judgement about her class's data probably being "more in the middle," but she is correct in thinking that a larger sample would increase the range of the data, as a larger sample might reveal that her classmates are more homogenous in comparison to other seventh-grade classes, if the population were defined as the country. The teacher might ask Nichole why she thinks her class is "more in the middle," and then ask the rest of the class to react to her conjecture. c. Charles is thinking about measures of center. The teacher might ask Charles to explain further what he means by "on average." Is he referring to the mode, the median, or the mean? d. Carl thinks that their sample is representative of the country if the country were defined as the population, but not if the population included seventh graders from other countries. The teacher might use this as an opportunity to discuss further reasons for defining the population being investigated.

 Session 10, Grades 6-8: Index | Notes | Solutions | Video