Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 12: Correlation

332

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334

Correlation Exercise 332

Solution SAQ 1

X and Y series show a perfect negative relationship between each other.

Solution SAQ 2

Solution SAQ 3

Solution SAQ 4

Solution SAQ 5

Solution SAQ 6

Economics (E)	Rank R₁	History (H)	Rank R₂	D= R₁ - R₂	D²
66	3	58	3.5	-5	0.25
90	1	76	1	0	0
89	2	65	2	0	0
55	5	58	3.5	1.5	2.25
58	4	53	6	-2	4
44	6	49	7	-1	1
42	7	56	5	2	4
N = 7					𝛴 D² = 11.50

58 is repeated two times in series 2. Thus, m₁= 2 and following formula is used to calculate correlation.

Solution SAQ 7

X	R₁	Y	R₂	D = R₁ - R₂	D²
80	1	12	8	-7	49
78	2	13	7	-5	25
75	3.5	14	5	-1.5	2.25
75	3.5	14	5	-1.5	2.25
58	8	14	5	3	9
67	5	16	2	3	9
60	6	15	3	3	9
59	7	17	1	6	36
N = 8					𝛴 D² = 141.5

75 is repeated two times in series 1 and 14 is repeated three times in series 2. Thus, m₁= 2 and m₂= 3 and following formula is used to calculate correlation.

Solution SAQ 8

Karl Pearson's Method:

Economics (X)	d_x = X - 35	d_x²	History (Y)	d_y = Y - 50	dy²	d_xd_y
77	42	1764	35	-15	225	-630
54	19	361	58	8	64	152
27	-8	64	60	10	100	-80
52	17	289	46	-4	16	-68
14	-21	441	50	0	0	0
35	0	0	40	-10	100	0
90	55	3025	35	-15	225	-825
25	-10	100	56	6	36	-60
56	21	441	44	-6	36	-126
60	25	625	42	-8	64	-200
N = 10	𝛴 d_x = 140	𝛴d_x² = 7110	N = 10	𝛴d_y = -34	𝛴dy² = 860	𝛴d_xd_y=-1837

Rank Difference Method:

Economics	R₁	History	R₂	D = R₁ - R₂	D²
77	2	35	9.5	-7.5	56.25
54	5	58	2	3	9
27	8	60	1	7	49
52	6	46	5	1	1
14	10	50	4	6	36
35	7	40	8	-1	1
90	1	35	9.5	-8.5	72.25
25	9	56	3	6	36
56	4	44	6	-2	4
60	3	42	7	-4	16
N = 10					𝛴D² = 280.5

35 is repeated two times in series 2. Thus, m₁= 2 and following formula is used to calculate correlation.

Correlation Exercise 333

Solution SAQ 9

Teaching Method	Rank of A R_A	Rank of B R_B	D = R_A - R_B	D²
I	2	1	1	1
II	1	3	-2	4
III	5	2	3	9
IV	3	4	-1	1
V	4	7	-3	9
VI	7	5	2	4
VII	6	6	0	0
N=7				𝛴D² = 28

Solution SAQ 10

Examples of perfect correlation:

Relationship between study hours and marks
Relationship between consumption and saving from fixed income
Relationship between amount of loan taken from bank and interest paid

X	R₁	Y	R₂	D=R₁- R₂	D²
48	3	13	5.5	-2.5	6.25
33	5	13	5.5	-0.5	0.25
40	4	22	1	3	9
9	9	6	8.5	0.5	0.25
16	7	14	4	3	9
65	1	20	2	-1	1
26	6	9	7	-1	1
15	8	6	8.5	-0.5	0.25
57	2	15	3	0.1	1
N = 9					𝛴 D² = 28

13 and 6 are repeated two times in series 2. Thus, m₁= 2 and m₂= 2 and following formula is used to calculate correlation.

Solution SAQ 11

X	d_x = X - 10	d_x²	Y	d_y = Y - 11	d_y²	d_xd_y
10	0	0	9	-2	4	0
6	-4	16	4	-7	49	28
9	-1	1	6	-5	25	5
10	0	0	9	-2	4	0
12	2	9	11	0	0	0
13	3	4	13	2	4	6
11	1	1	8	-3	9	-3
9	-1	1	4	-7	49	7
N = 8	𝛴d_x = 0	𝛴d_x² = 32	N = 8	𝛴d_y = -24	𝛴d_y² = 144	𝛴d_xd_y = 43

Solution SAQ 12

d_x	d_x²	d_y	d_y²	d_xd_y
5	25	5	25	25
-4	16	-12	144	48
-2	4	-7	49	14
20	400	25	625	500
-10	100	-10	100	100
0	0	-3	9	0
3	9	0	0	0
0	0	2	4	0
-15	225	-9	81	135
-5	25	-15	225	75
𝛴 d_x = -8	𝛴 d_x² = 804	𝛴 d_y = -24	𝛴 d_y² = 1262	𝛴 d_xd_y = 897

Solution SAQ 13

Entry	Judge X (R_X)	Judge Y (R_Y)	D = R_X - R_Y	D²
A	1	12	-11	121
B	2	9	-7	49
C	3	6	-3	9
D	4	10	-6	36
E	5	3	2	4
F	6	5	1	1
G	7	4	3	9
H	8	7	1	1
I	9	8	1	1
J	10	2	8	64
K	11	11	0	0
L	12	1	11	121
N = 12				𝛴 D² = 416

Solution SAQ 14

R_X	R_Y	D = R_X - R_Y	D²
8	7	1	1
7	5	2	4
6	4	2	4
3	1	2	4
2	3	-1	1
1	2	-1	1
5	6	-1	1
4	8	-4	16
			𝛴D² = 32

Solution SAQ 15

R₁	R₂	R₃	D₁ = R₁- R₂	D₂ = R₁ - R₃	D₃ = R₂ - R₃	D₁²	D₂²	D₃²
1	3	6	-2	-5	-3	4	25	9
6	5	4	1	2	1	1	4	1
5	8	9	-3	-4	-1	9	16	1
10	4	8	6	2	-4	36	4	16
3	7	1	-4	2	6	16	4	36
2	10	2	-8	0	8	64	0	64
4	2	3	2	1	-1	4	1	1
9	1	10	8	-1	-9	64	1	81
7	6	5	1	2	1	1	4	1
8	9	7	-1	1	8	1	1	64
						𝛴D₁²= 200	𝛴D₂² = 60	𝛴D₃² = 214

Judges I and III have a common taste in respect of beauty as they have the highest positive rank correlation coefficient.

Correlation Exercise 334

Solution SAQ 16

Solution SAQ 17

Age Group	Mid Value (X)	Percentage of Players (%) (Y)	d_X = X-17.5	d_Y = Y-40	d_Xd_Y	d_X²	d_Y²
15-16	15.5	200/250×100 = 80	-2	40	-80	4	1600
16-17	16.5	150/2-00×100 = 75	-1	35	-35	1	1225
17-18	17.5	90/150×100 = 60	0	20	0	0	400
18-19	18.5	48/120×100 = 40	1	0	0	1	0
19-20	19.5	30/100×100 = 30	2	-10	-20	4	100
20-21	20.5	12/80×100 = 15	3	-25	-75	9	625
	N = 6		𝛴d_X = 3	𝛴d_Y = 60	𝛴 d_Xd_Y = -210	𝛴d_X² = 19	𝛴 d_Y² = 𝛴3950

Solution SAQ 18

Density (X)	dx = X - 500	dx²		dy = Y-1	dy²	dxdy
200	-300	90000	2	1	1	-300
500	0	0	1	0	0	0
700	200	40000	1.3	0.3	0.09	60
500	0	0	1.4	0.4	0.16	0
600	100	10000	1.6	0.6	0.36	60
900	400	160000	1.7	0.7	0.49	280
	𝛴dx=400	𝛴dx²=300000		𝛴dy=3	𝛴dy² = 2.1	𝛴dxdy = 100

Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 12: Correlation

Correlation Exercise 332

Solution SAQ 1

Solution SAQ 2

Solution SAQ 3

Solution SAQ 4

Solution SAQ 5

Solution SAQ 6

Solution SAQ 7

Solution SAQ 8

Correlation Exercise 333

Solution SAQ 9

Solution SAQ 10

Solution SAQ 11

Solution SAQ 12

Solution SAQ 13

Solution SAQ 14

Solution SAQ 15

Correlation Exercise 334

Solution SAQ 16

Solution SAQ 17

Solution SAQ 18

Solution SAQ 19

Solution SAQ 20

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Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 12: Correlation

Correlation Exercise 332

Solution SAQ 1

Solution SAQ 2

Solution SAQ 3

Solution SAQ 4

Solution SAQ 5

Solution SAQ 6

Solution SAQ 7

Solution SAQ 8

Correlation Exercise 333

Solution SAQ 9

Solution SAQ 10

Solution SAQ 11

Solution SAQ 12

Solution SAQ 13

Solution SAQ 14

Solution SAQ 15

Correlation Exercise 334

Solution SAQ 16

Solution SAQ 17

Solution SAQ 18

Solution SAQ 19

Solution SAQ 20

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