Question

How much time do Americans living in or near cities spend waiting in traffic, and how much does waiting in traffic cost them per year? The data set given includes this cost for 31 cities. For the time Americans living in or near cities spend waiting in traffic and the cost of waiting in traffic per year:

a. Compute the mean, median, first quartile, and third quartile.

b. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.

c. Construct a boxplot. Are the data skewed? If so, how?

d. Compute the correlation coefficient between the time spent sitting in traffic and the cost of sitting in traffic.

e. Based on the results of (a) through (c), what conclusions might you reach concerning the time spent waiting in traffic and the cost of waiting in traffic.

City	Annual Time Sitting in Traffic (hours)	Cost of Sitting in Traffic ($)
Boston	47	980
New York	54	1126
Philadelphia	42	864
Washington	74	495
Miami	38	785
Detroit	33	687
Cleveland	20	383
Minneapolis	45	916
Milwaukee	27	541
Chicago	71	1568
St. Louis	30	642
Nashville	35	722
Memphis	23	477
Atlanta	43	824
New Orleans	35	746
Omaha	21	389
Wichita	20	379
Dallas	45	924
Houston	57	1171
Denver	49	993
Albuquerque	25	525
Phoenix	35	821
Salt Lake City	27	512
Las Vegas	28	512
Boise	19	345
Seattle	44	942
Portland	37	744
San Francisco	50	1019
San Jose	37	721
Los Angeles	64	1334
San Diego	38	794

Answer 1

a.

(i) Annual Time Sitting in Traffic (hours)

Mean is given as,

= 1213/31

= 39.13

Median is given as,

Median = 37

Note : The median is calculated as the middling value. Since there are 31 data vlaues, the ((31+1)/2)16th values is the median.

First Quartile: Q1 = ((n+1)*0.25)th value = 8th term = 27

Third Quartile: Q3 = ((n+1)*0.75)th value = 24th term = 47

(ii) Cost of Sitting in Traffic ($)

Mean is given as,

= 23881/31

= 770.35

Median is given as,

Median = 746

Note : The median is calculated as the middling value. Since there are 31 data vlaues, the ((31+1)/2)16th values is the median.

First Quartile: Q1 = ((n+1)*0.25)th value = 8th term = 512

Third Quartile: Q3 = ((n+1)*0.75)th value = 24th term = 942

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b.

(i)  Annual Time Sitting in Traffic (hours)

Range = Maximum value - Minimum Value

= 74 - 19

= 55

Interquartile range

IRQ = Q3 -Q1

= 20

Variance is given as,

where,

n = 31

therefore,

s2 = 210.38

Standard deviation is given as,

=  14.50

Coefficient of variation is given as,

= 0.3707

(ii) Cost of Sitting in Traffic ($)

Range = Maximum value - Minimum Value

= 345 - 1568

= 1223

Interquartile range

IRQ = Q3 -Q1

= 430

Variance is given as,

where,

n = 31

therefore,

s2 = 85092.24

Standard deviation is given as,

=  291.705

Coefficient of variation is given as,

= 0.3786

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c.

(i) Annual Time Sitting in Traffic (hours)

(ii) Cost of Sitting in Traffic ($)

Yes, the data is skewed. The data are right skewed as seen in the above boxplots. The (Q3 + 1.5 IRQ) is far from the median in both the cases therefore the values towards right vary in large magnitufde then on the left.

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d.

The correlation coefficient is,

the given data is,

The calculations are given as,

where Mx = 39.129

My = 770.35

Therefore, the coefficient of correlation, r = -0.0245

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e.

Based on the results of (a) through (c), we can conclude that there is positive linear correlation between Annual Time Sitting in Traffic and Cost of Sitting in Traffic ($). Spending more time in traffic costs more when compared to speding less time in traffic.