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Data Session 10, Notes
 
Session 10 Session 10 3-5 Part A Part B Part C Part D Homework
 
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A B C D

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Solutions for Session 10, Part D

See solutions for Problems: D1 | D2 | D3


Problem D1

a. 

Damon is focusing on the extreme values and the range. The teacher could reinforce the meaning of range.

b. 

Juanita incorrectly reasons that 64 is an outlier because there is no data point at 63. However, with 64 separated by only one inch from the other values, it is not unusual enough to be considered an outlier. The teacher might ask the rest of the class to discuss further the meaning of an outlier.

c. 

Asher incorrectly reasons that there can be a mode only when one value has more data points than any other value. In this example, 55 and 56 are both considered modes. The teacher might use this as an opportunity to discuss the meaning of mode.

d. 

Larie is looking at an interval of the range where most of the data is concentrated. The teacher might ask Larie to explain how she reached this conclusion and then ask the class to consider why it can be helpful to look at these smaller intervals of concentrated data.

e. 

Michael incorrectly reasons that 58 is the median by finding the middle of the range from 52 to 64 instead of the middle of the data points. The teacher might begin by reviewing the meaning of median and then ask all the children to line up from shortest to tallest and, using themselves, find the median. Now the class would need to discuss the discrepancy between the median Michael proposed and the one the class found.

f. 

Ali incorrectly thinks the range comprises all the numbers shown on the line plot, even when the numbers do not contain any values. This error arises if students are accustomed to seeing line plots that almost always begin and end with values that contain data. The teacher could use the following questioning to get Ali to focus on the data points: "What is the smallest height of someone in our class? Point to it on the line plot with your left hand. What is the tallest height of someone in our class? Point to it with your right hand. This distance from the lowest to the highest number is what we call the range."

g. 

Antrell correctly reasons about the median and finds it accurately. The teacher might want Antrell to show the class how he found the median and then ask the class to consider why it is important to find the median of a data set.

<< back to Problem D1


 

Problem D2

a. 

Ava is thinking about the whole set of data about first graders in comparison to the fourth graders' set of data. The teacher might ask other students whether they agree and to explain why or why not.

b. 

Nichole is thinking about the spread of the data the class will collect. The teacher could ask the students to consider the spread of their own height data and to quantify their predictions for the range of height data of the first graders.

c. 

Houa is thinking about the range of the data the class will collect. The teacher might ask the students to get out some measuring tapes and mark on the wall the heights from 40 to 50; once the children have looked at these heights, the teacher can ask them to react to Houa's statement.

d. 

Charles is thinking about a specific value, most likely the mode. The teacher might ask Charles if he thinks all first graders, a few of them, or most of them will be three feet tall.

<< back to Problem D2


 

Problem D3

a. 

Asher does not define "lots," nor does she mention that one of the first graders is as tall as a fourth grader. The teacher could ask Asher to explain what she means by "lots" and ask whether all the first graders are shorter than all the fourth graders.

b. 

Charles is reasoning by focusing on the mode of 42 inches. The teacher could reinforce the meaning and use of the term mode.

c. 

Ali is quantifying "how much taller" the fourth graders are than the first graders by comparing the modes of the data sets. The teacher might ask Ali why she compared the modes and then ask the rest of the class to consider the advantages and disadvantages of this approach.

d. 

Nichole is quantifying "how much taller" the fourth graders are than the first graders by comparing the medians of the data sets. The teacher might ask Nichole why she compared the medians and then ask the rest of the class to consider the advantages and disadvantages of this approach as compared to using the modes.

e. 

Tarra is comparing the data sets and thinking about outliers as she reasons that it is unusual for a first grader to be 52 inches tall. This would be an opportunity to discuss further the meaning of outlier.

f. 

Juanita is comparing the range of the two data sets. The teacher could ask Juanita to explain how she reached this conclusion and what this tells us about the heights of first graders.

g. 

Larie is thinking about intervals of the data that contain most of the data. The teacher might use this as an opportunity to focus further attention on the importance of examining intervals when considering how the data are spread out or bunched together.

<< back to Problem D3


 

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