Question

Recall that the quartiles for sample data are obtained by dividing the number of ordered observations into two equal parts: a lower half and an upper half.

We are given the following data.

Urban Area	Total Cost (millions of dollars)
New York	17
Los Angeles	15
Chicago	9
Washington, D.C.	7
Houston	7
Dallas/Fort Worth	5
Detroit	5
Miami	5
Phoenix	5
Philadelphia	5
San Francisco	4
Boston	4
Atlanta	4

To find the values of the lower quartile and the upper quartile, we must first order the data set of the estimated traffic congestion cost (in millions of dollars) for different urban areas from the least to greatest.

4, 4, 4, 5, 5, 5, 5,  , 7, 7, 9,  , 17

Now that we have ordered the values from least to greatest, we must now split the data into two equal parts. Recall that if the total number of ordered observations is odd, then the median is excluded from both halves.

The total number of observations in the data set is  . The median value (the middle value in the ordered set) is $  million. Since the number of ordered observations is  ---Select--- odd even , the median value  ---Select--- should not should be excluded.

Answer 1

To find the values of the lower quartile and the upper quartile, we must first order the data set of the estimated traffic congestion cost (in millions of dollars) for different urban areas from the least to greatest.

4, 4, 4, 5, 5, 5, 5, 5, 7, 7, 9, 15, 17

Now that we have ordered the values from least to greatest, we must now split the data into two equal parts. Recall that if the total number of ordered observations is odd, then the median is excluded from both halves.

The total number of observations in the data set is 13. The median value (the middle value in the ordered set) is $5 million. Since the number of ordered observations is odd , the median value should be excluded.

To find the lower quartile:

Bottom half:

4, 4, 4, 5, 5, 5

Middle of these numbers = (4 + 5)/2 = 4.5

So,

the lower quartile = 4.5

To find the upper quartile:

Upper half:

5, 7, 7, 9, 15, 17

The middle of these numbers = (7 + 9)/2= 8

So,

the upper quartile = 8