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. |
