Chapter 10.4, Problem 3IP

To determine

To calculate: The centers and variations and write an inference about the two populations.

Answer to Problem 3IP

The waiting time at Lucy’s steak house have a median of 20 minutes with an inter quartile range of 20 minutes.

The waiting time at Gary’s grill have a median of 15 minutes with an inter quartile range of 10 minutes.

The waiting time at Lucy’s steak house is greater. The customer will wait more at Lucy’s steak house.

Explanation of Solution

Given information: The double box plot showing the average waiting times on the two restaurants Lucy’s steak house and Gary’s grill.

Calculation:

Both the distributions are not symmetric. Use the median to compare the centers and the inter quartile range to compare the variations.

In a box plot, a box is drawn from the first quartile to the third quartile and median is where the vertical line goes through.

For Lucy’s steak house:

  $median=20$

  $\text{Left quartile}=10$

  $\text{Right quartile=30}$

Therefore, $$

  $\text{inter quartile}=\text{ right quartile}-\text{ left quartile}$

  $\text{inter quartile}=\text{ 3}0-10$

  $\text{inter quartile}=\text{ 20}$

The waiting time at Lucy’s steak house have a median of 20 minutes with an inter quartile range of 20 minutes.

For Gary’s grill:

  $median=15$

  $\text{Left quartile}=10$

  $\text{Right quartile=20}$

Therefore, $$

  $\text{inter quartile}=\text{ right quartile}-\text{ left quartile}$

  $\text{inter quartile}=\text{ 20-10}$

  $\text{inter quartile}=\text{ 10}$

The waiting time at Gary’s grill have a median of 15 minutes with an inter quartile range of 10 minutes.

	Lucy’s steak house	Gary’s grill
median	20	15
inter quartile range	20	10

The waiting time at Lucy’s steak house is greater. The customer will wait more at Lucy’s steak house.