b How do you define reliability? Low IQR or low standard deviation?
A
a See solution.
B
b It depends on what he is looking for.
Practice makes perfect
a To make any deductions, we first have to enter the values into lists. Push STAT, choose Edit, and then enter the values in the first two columns.
Having entered the values, we have to instruct the calculator that we want to graph a combination histogram and boxplot. Push 2nd and Y=, and choose one of the plots in the list. Make sure you turn the plot ON, choose the type to boxplot, and assign L1 as XList.
In the same diagram, we also want to include a histogram of Chip W. Therefore, push 2nd and Y=, and choose one of the plots in the list. Make sure you turn the plot ON, choose the type to boxplot, and assign L2 as XList.
Finally, to graph the combination, push GRAPH. Note that you may need to change the x-axis so that it spans the length of the boxplot and histogram.
Let's repeat the procedure for Chip Z by changing Plot 1 and Plot 2 to use the values from L2 instead.
When we compare the diagrams of the two memory chips, we see that Chip W has a greater interquartile range. On the other hand, Chip Z has observations that are farther away from the center. This affects the standard deviation, but not the interquartile range.
Why can they be conflicting?
The two measures can be conflicting because they are both measures of spread, but they can tell very different stories about the dataset.
b It depends on what Duncan is looking for. If he chooses Chip W, he will have a low standard deviation. If he chooses Chip Z, he will have a low interquartile range. Therefore, it depends on how he defines reliability.
