Chapter 10.4, Problem 6IP

To determine

To calculate: The centers and variations and to find which airline had shorter flight time.

Answer to Problem 6IP

Air jet Express has a median of 4 hours with an inter quartile range 4 hours.

Cross Country Airlines has a median of 5 hours with an inter quartile range 2 hours.

Air jet Express has a shorter time of flight.

Explanation of Solution

Given information: The double dot plots shows the flight times of two different airlines, Air jet Express and Cross Country Airlines.

Calculation:

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

Air jet express:

First finding the median of,

  $2,2,3,3,3,4,4,5,7,8,8$

The median is the middle number.

  $Median=4$

Now finding the quartiles.

The first quartile $Q_1$ is the median of points to the left of the median.

  $2,2,3,3,3$

  $Q_1=3$

The third quartile $Q_3$ is the median of points to the right of the median.

  $4,5,7,8,8$

  $Q_3=7$

The inter quartile range is,

  $\text{inter quartile range}=Q_3-Q_1$

  $\text{inter quartile range}=7-3$

  $\text{inter quartile range}=4$

Air jet Express has a median of 4 hours with an inter quartile range 4 hours.

Cross Country Airlines:

First finding the median of,

  $3,3,4,4,5,5,5,6,6,7,7$

The median is the middle number.

  $Median=5$

Now finding the quartiles.

The first quartile $Q_1$ is the median of points to the left of the median.

  $3,3,4,4,5$

  $Q_1=4$

The third quartile $Q_3$ is the median of points to the right of the median.

  $5,6,6,7,7$

  $Q_3=6$

The inter quartile range is,

  $\text{inter quartile range}=Q_3-Q_1$

  $\text{inter quartile range}=6-4$

  $\text{inter quartile range}=2$

Cross Country Airlines has a median of 5 hours with an inter quartile range 2 hours.

The inter quartile range of Air jet Express is greater than that of Cross Country Airlines. However, the median of Air jet Express is less than that of Cross Country Airlines.

Therefore Air jet Express has a shorter time of flight.