Chapter 12.4, Problem 24PPE

a.

To determine

To find: The device which produces packages with more consistent weights.

Answer to Problem 24PPE

Device $1$.

Explanation of Solution

Given information:

A box-and-whisker plot is given below which represents the weights of the bags packed by two different packaging device.

  

Calculation:

A box-and-whisker plot is given below which represents the weights of the bags packed by two different packaging device.

  

From above plot, it is observed that the interquartile range (IQR) for device 1 is less than the device $2$ . This means weights of the boxes packed by device $1$ are more close to each other, in other words more consistent.

b.

To determine

To find: The preferred device for the desired result.

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

A box-and-whisker plot is given below which represents the weights of the bags packed by two different packaging device.

  

From above plot, it is observed that the interquartile range (IQR) for device 1 is less than the device $2$ . This means weights of the boxes packed by device $1$ are more close to each other, in other words more consistent.

Box-and-whisker represents the percentage of data values. From minimum to first quartile $25\%$ of data values lie, from first quartile to third quartile $50\%$ of data values and from third quartile to maximum rest $25\%$ of data values lie.

Therefore, to minimize the packaged boxes with weights less than $17$ oz, device $2$ should be chosen. Since device $2$ has less percentage of data value in less than $17$ ozrange.

Similarly, to minimize the packaged boxes with weights more than $17$ oz, device $1$ should be chosen. Since device $1$ has less percentage of data value in more than $17$ ozrange.