Duncan is testing two types of memory chips ($W$ and $Z$) for performance and reliability. One test involves a measurement of the maximum electrical current in milliamperes required by the chip when storing and retrieving $14$ different data sets. A lower required current means greater energy efficiency.   

Data Set:

1. When Duncan is trying to summarize the data, he finds the IQR for chip $W$ is larger, but the standard deviation for chip $Z$ is larger. Both are measures of spread. How can they be conflicting? Use combination histogram and boxplots in your explanation.

   Hint (a):

   The IQR can be seen on the boxplot as the length of the box portion.
   Does the boxplot for chip $Z$ have a larger box than the boxplot for chip $W$?
   Outliers affect standard deviation, but not the IQR.
   Does chip $Z$ have more outliers than chip $W$?

2. Which chip should Duncan recommend to the manufacturer? Justify your choice.

   Hint (b):

   Which chip has a lower average energy use? Is it consistent?
   Does each seem to have its benefits and drawbacks?

   Answer (b):

   Chip $Z$ tends to be more energy efficient. It also has a smaller IQR.
   However, it has outliers, so these could indicate a reliability problem.

   Explore using the eTool below .
   Click the link to the right for full version. 11-103 HW eTool