Question

In: Math

Income Person (Yi) F(Yi) 1 79.6 0.1 2 138.7 0.2 3 173.1 0.3 4 187.8 0.4...

Income

Person	(Yi)	F(Yi)
1	79.6	0.1
2	138.7	0.2
3	173.1	0.3
4	187.8	0.4
5	201.3	0.5
6	226.6	0.6
7	247.4	0.7
8	289.2	0.8
9	322.8	0.9
10	587.9	1

A. The mean or average of the ranked above data for a village in Peru is:

a. $245.44

b. $345.44

c. $123.44

d. $200.56

B. Suppose that the covariance between the ranked income and the cumulative distribution of income is 33.24. The Gini coefficient for this village is approximately:

a. .212
b. .223

c. .271

d. .281

Solutions

Expert Solution

solution:

A answer:

mean or average=xi/n

= (79.6+138.7+173.1+187.8+201.3+226.6+247.4+289.2+322.8+587.9)/10

=2454.4/10

mean or average = $245.44

hence,the mean or average of the ranked above data for a village in peru is 245.44

from given options the option' (a)' is correct.

(B) answer:

here we have to find the covariance between Yn and F(YN) fromthe table.

we know that

the formula for covariance is given by

covariance=mean[Yn=mean(F(Yn)]

Mean	245.44
Mean(F(Yn))	=0.55

now to draw the table it shows the covariance was obtained.which is already mentioned in the

questionas33.24

person	income(Y)	F(Y)	F(Yn)-mean(F(Yn))	F(Yn)-mean(F(Yn))	Yn-mean(Yn)*F(Yn)-mean(F(Yn))
1	79.6	0.1	-165.84	-0.45	74.628
2	138.7	0.2	-106.74	-0.35	37.359
3	173.1	0.3	-72.34	-0.25	18.085
4	187.8	0.4	-57.s64	-0.15	8.646
5	201.3	0.5	-44.14	-0.05	-0.942
6	226.6	0.6	-18.84	0.05	-0.942
7	247.4	0.7	1.96	0.15	0.294
8	289.2	0.8	43.76	0.25	10.94
9	322.8	0.9	77.36	0.35	27.076
10	587.9	1	342.46	0.45	154.107
					33.24

G=2*COV(Yn,F(Yn))/mean

from the formula

G=(2*33.24)/mean(Yn)

G=66.48/245.44

G=0.271

Hence the correct option is 'C'

milcah answered 4 months ago

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