### Home > CCA > Chapter 11 > Lesson 11.3.3 > Problem11-103

11-103.

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

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 1873

Chip Z

129

131

131

132

132

132

133

133

133

133

134

137

138

140

checksum 1868

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.

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.

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

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