Chapter 10.4, Problem 2GP

To determine

To calculate: The centers and variations and to find on which road speeds are more consistent.

Answer to Problem 2GP

The speeds in Hayes Road has a median of 55 miles per hour with an inter quartile range of 10 miles per hour.

The speeds in Jefferson Road has a median of 45 miles per hour with an inter quartile range of 15 miles per hour.

Hayes Road speeds are more consistent.

Explanation of Solution

Given information: The double box plots showing the speed of cars at two different roads.

Calculation:

The distribution for speeds in Hayes Road is symmetric, while that of speeds in Jefferson Road is not symmetric. Use the median to compare the centers and the inter quartile range to compare the variations.

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

For Hayes Road:

  $median=55$

  $\text{Left quartile}=50$

  $\text{Right quartile=60}$

Therefore, $$

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

  $\text{inter quartile}=\text{ 60-50}$

  $\text{inter quartile}=\text{ 10}$

The speeds in Hayes Road has a median of 55 miles per hour with an inter quartile range of 10 miles per hour.

For Jefferson Road:

  $median=45$

  $\text{Left quartile}=40$

  $\text{Right quartile=55}$

Therefore, $$

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

  $\text{inter quartile}=\text{ 55-40}$

  $\text{inter quartile}=\text{ 15}$

The speeds in Jefferson Road has a median of 45 miles per hour with an inter quartile range of 15 miles per hour.

	Hayes Road	Jefferson Road
median	55	45
inter quartile range	10	15

Median of Hayes Road speeds are greater than that of Jefferson Road with little variation.

So, Hayes Road speeds are more consistent.