CPM Homework Help : INT1 Problem 10-106

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:
	A	B	C	D	E	F	G	H	I	J	K	L	M	N
Chip W	$130$	$130$	$132$	$132$	$133$	$133$	$133$	$134$	$135$	$135$	$135$	$137$	$137$	$137$
												checksum $\mathit{1873}$
Chip Z	$129$	$131$	$131$	$132$	$132$	$132$	$133$	$133$	$133$	$133$	$134$	$137$	$138$	$140$
												checksum $\mathit{1868}$

When Duncan was trying to summarize the data, he found the IQR for chip W is larger, but the standard deviation for chip Z was 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 W have a larger box than the boxplot for chip Z?
Outliers affect standard deviation, but not the IQR.
Does chip W have more outliers than chip Z?
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 it 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.

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