Question

QUESTION 9 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 file here contains this cost for 30 cities. For the cost sitting in traffice, compute the balancing point, the value that occurs more than any other, the middle value, the standard deviation, skewness, kurtosis, coefficient of variation and range Balancing point The value that occurs more than any other = The middle value Standard deviation Skewness Kurtosis Coefficient of variation % Range Answers should be accurate up to 2 decimal places. Remember that coefficient of variation is measured in percentages.

Answer 1

Balancing point is the mean

Ση теаn п

= 23386/30

= 779.53

Value that occurs more than any other value is the mode

Mode =512

Note : we can see that 512 has occurred twice but other values are not repeated

Middle value is the median

n=30 , median is the mean of 15th and 16th observation after arranging in ascending order

Median =(746+785)/2 = 765.5

345
379
383
389
477
512
512
525
541
642
687
721
722
744
746
785
794
821
824
864
916
924
942
980
993
1019
1126
1171
1334
1568

Standard deviation is given by

-mean)2/(n - S =

Calculation

	x	(x-xbar)^2
	345	188816.3
	379	160424.3
	383	157236
	389	152513.7
	477	91524.4
	512	71572.3
	512	71572.3
	525	64785.52
	541	56896.56
	642	18914.5
	687	8561.801
	721	3425.761
	722	3309.701
	744	1262.381
	746	1124.261
	785	29.9209
	794	209.3809
	821	1719.761
	824	1977.581
	864	7135.181
	916	18624.06
	924	20871.58
	942	26396.5
	980	40188.22
	993	45569.44
	1019	57345.88
	1126	120041.5
	1171	153248.8
	1334	307437
	1568	621684.9
total		2474419

2474419/29 s =

= 292.10

Skewness is given by

Lt - теan)3 Sk (п — 1)s3

calculation

	x	(x-xbar)^3
	345	-82046355.9
	379	-64254737.2
	383	-62348807.3
	389	-59561167.8
	477	-27688877
	512	-19147737.7
	512	-19147737.7
	525	-16489858.6
	541	-13571536.7
	642	-2601311.31
	687	-792223.437
	721	-200509.785
	722	-190407.093
	744	-44852.3934
	746	-37696.468
	785	163.667323
	794	3029.741623
	821	71318.48452
	824	87943.02262
	864	602708.7306
	916	2541625.591
	924	3015317.293
	942	4288639.501
	980	8056532.644
	993	9727708.549
	1019	13732618.1
	1126	41590764.96
	1171	59992292.43
	1334	170464582.8
	1568	490179925.4
total		436231354.5

436231354 Sk (30 1)292.103

= 0.60

Kurtosis is given by

(x - Er-mean) (n 1)st kurtosis

calculation

	x	(x-xbar)^4
	345	35651603038
	379	25735949902
	383	24723172558
	389	23260422862
	477	8376715960
	512	5122594256
	512	5122594256
	525	4197163718
	541	3237218642
	642	357758344.3
	687	73304434.65
	721	11735837.74
	722	10954120.05
	744	1593605.537
	746	1263962.571
	785	895.2602568
	794	43840.36128
	821	2957577.553
	824	3910826.216
	864	50910806.48
	916	346855644.4
	924	435622889.3
	942	696775259.8
	980	1615093099
	993	2076573944
	1019	3288550056
	1126	14409952335
	1171	23485182717
	1334	94517497225
	1568	3.86492E+11
total		6.63306E+11

kurtosis = 3.14

Coefficient of variation

S CV = (- mean

100

= (292.10/779.53)*100%

= 37.47 %

Range = highest observation -lowest observation

= (1568-345)

= 1223