Question

In: Statistics and Probability

Refer to the traffic congestion cost table as the primary source of your observations, and do...

Refer to the traffic congestion cost table as the primary source of your observations, and do the followings;

1. Summarize the cost by calculating the mean and standard deviation for each region

2. Calculate the Standard deviation for all five regions ONLY TYPED HARD COPY IS ACCEPTED

3. Use a bar graph for this data set and show the five averages on the graph

4. List all the averages and standard deviations of five regions for comparison

	City	Cost Traffic
Northeastern cities	Baltimore, MD	530
	Boston, MA	880
	Hartford, CT	250
	New York, NY	1,090
	Philadelphia, PA	420
	Pittsburgh, PA	400
	Washington, DC	1,420
Midwestern cities	Chicago, IL	570
	Cincinnati, OH	200
	Cleveland, OH	140
	Columbus, OH	230
	Detroit, MI	530
	Indianapolis, IN	130
	Kansas City, MO	160
	Louisville, KY	190
	Milwaukee, WI	370
	Minneapolis-St. Paul, MN	270
	Oklahoma City, OK	190
	St. Louis, MO	540
Southern cities	Atlanta, GA	640
	Charlotte, NC	390
	Ft. Lauderdale, FL	290
	Jacksonville, FL	400
	Memphis, TN	140
	Miami, FL	680
	Nashville, TN	340
	New Orleans, LA	340
	Norfolk, VA	390
	Orlando, FL	420
	Tampa, FL	310
Southwestern cities	Albuquerque, NM	210
	Austin, TX	410
	Corpus Christi, TX	50
	Dallas, TX	750
	Denver, CO	420
	El Paso, TX	120
	Fort Worth, TX	420
	Houston, TX	750
	Phoenix, AZ	630
	Salt Lake City, UT	90
	San Antonio, TX	290
Western cities	Honolulu, HI	470
	Los Angeles, CA	980
	Portland, OR	500
	Sacramento, CA	280
	San Bernardino-River, CA	1,320
	San Diego, CA	480
	San Francisco-Oakland, CA	930
	San Jose, CA	960
	Seattle-Everett, WA	880

Expert Solution

1. Mean by region is equal to the total cost of traffic across all citities in the region divided by the total no of cities in that region.

e.g Like for North Eastern cities , the Total cost of traffic =(530+880+250+1090+420+400+1420)/7

=4990/7

=712.9

Assuming that the cities in each region are only cities and represent entire population

Standard Deviation= sqrt(((530-Mean)2+(880-Mean)2+(250-Mean)2+(1090-Mean)2+(420-Mean)2+(400-Mean)2+(1420-Mean)2)/7)

=sqrt(((530-712.9)2+(880-712.9)2+(250-712.9)2+(1090-712.9)2+(420-712.9)2+(400-712.9)2+(1420-712.9)2)/7)

=396.7

Regions	City	Cost Traffic	Mean	Standard Deviation
Northeastern cities	Baltimore, MD	530	712.9	396.7
Boston, MA	880
Hartford, CT	250
New York, NY	1,090
Philadelphia, PA	420
Pittsburgh, PA	400
Washington, DC	1,420
Midwestern cities	Chicago, IL	570	293.3	158.6
Cincinnati, OH	200
Cleveland, OH	140
Columbus, OH	230
Detroit, MI	530
Indianapolis, IN	130
Kansas City, MO	160
Louisville, KY	190
Milwaukee, WI	370
Minneapolis-St. Paul, MN	270
Oklahoma City, OK	190
St. Louis, MO	540
Southern cities	Atlanta, GA	640	394.5	145.0
Charlotte, NC	390
Ft. Lauderdale, FL	290
Jacksonville, FL	400
Memphis, TN	140
Miami, FL	680
Nashville, TN	340
New Orleans, LA	340
Norfolk, VA	390
Orlando, FL	420
Tampa, FL	310
Southwestern cities	Albuquerque, NM	210	376.4	252.6
Austin, TX	410
Corpus Christi, TX	50
Dallas, TX	750
Denver, CO	420
El Paso, TX	120
Fort Worth, TX	420
Houston, TX	750
Phoenix, AZ	630
Salt Lake City, UT	90
San Antonio, TX	290
Western cities	Honolulu, HI	470	755.6	317.2
Los Angeles, CA	980
Portland, OR	500
Sacramento, CA	280
San Bernardino-River, CA	1,320
San Diego, CA	480
San Francisco-Oakland, CA	930
San Jose, CA	960
Seattle-Everett, WA	880

2. Standard Deviation of all 5 regions, for that we have to first find the mean of all 5 regions taken together

Mean of all 5 regions taken together= 475.8

Applying the formula above for Standard Deviation

Regions	City	Cost Traffic
Northeastern cities	Baltimore, MD	530
Boston, MA	880
Hartford, CT	250
New York, NY	1,090
Philadelphia, PA	420
Pittsburgh, PA	400
Washington, DC	1,420
Midwestern cities	Chicago, IL	570
Cincinnati, OH	200
Cleveland, OH	140
Columbus, OH	230
Detroit, MI	530
Indianapolis, IN	130
Kansas City, MO	160
Louisville, KY	190
Milwaukee, WI	370
Minneapolis-St. Paul, MN	270
Oklahoma City, OK	190
St. Louis, MO	540
Southern cities	Atlanta, GA	640
Charlotte, NC	390
Ft. Lauderdale, FL	290
Jacksonville, FL	400
Memphis, TN	140
Miami, FL	680
Nashville, TN	340
New Orleans, LA	340
Norfolk, VA	390
Orlando, FL	420
Tampa, FL	310
Southwestern cities	Albuquerque, NM	210
Austin, TX	410
Corpus Christi, TX	50
Dallas, TX	750
Denver, CO	420
El Paso, TX	120
Fort Worth, TX	420
Houston, TX	750
Phoenix, AZ	630
Salt Lake City, UT	90
San Antonio, TX	290
Western cities	Honolulu, HI	470
Los Angeles, CA	980
Portland, OR	500
Sacramento, CA	280
San Bernardino-River, CA	1,320
San Diego, CA	480
San Francisco-Oakland, CA	930
San Jose, CA	960
Seattle-Everett, WA	880
	Mean	475.8
	Standard Deviation	311.7

3.

4.

Regions	Mean	Standard Deviation
Northeastern cities	712.9	396.7
Midwestern cities	293.3	158.6
Southern cities	394.5	145.0
Southwestern cities	376.4	252.6
Western cities	755.6	317.2

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