The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.
Student A B C D E F G H I J K L
History 69 36 39 71 67 76 40 20 85 65 55 34
Mathematics 33 52 71 25 79 22 83 81 24 35 46 64

-0.77

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-0.92

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0.77

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.92

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Solution

The correct option is A -0.77

Students

History $(H)$

Mathematics $(M)$

Rank $(H)$

Rank $(M)$

$| d |$

$d^{2}$

A

B

C

D

E

F

G

H

I

J

K

L

69

36

39

71

67

76

40

20

85

65

55

34

33

52

71

25

79

22

83

81

24

35

46

64

4

10

9

3

5

2

8

12

1

6

7

11

9

6

4

10

3

12

1

2

11

8

7

5

5

4

5

7

2

10

7

10

10

2

0

6

25

6

25

49

4

100

49

100

100

4

0

36

$n = 12, \sum d^{2} = 508$

$r = 1 - \frac{6 \sum d^{2}}{n (n^{2} - 1)} = 1 - \frac{6 \times 508}{12 (12^{2} - 1)} = 1 - \frac{3048}{1716} = - 0.77$

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Similar questions

The marks in History and Mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.

Student	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$	$K$	$L$
History	$69$	$36$	$39$	$71$	$67$	$76$	$40$	$20$	$85$	$65$	$55$	$34$
Mathematics	$33$	$52$	$71$	$25$	$79$	$22$	$83$	$81$	$24$	$35$	$46$	$64$

Interpret the result.

Q. Calculate the correlation coefficient of the marks obtained by 12 students in Mathematics and Statistics and interpret it.

Students	:	A	B	C	D	E	F	G	H	I	J	K	L
Marks (in Maths)	:	50	54	56	59	60	62	61	65	67	71	71	74
Marks ( in Statis.)	:	22	25	34	28	26	30	32	30	28	34	36	40

Q. The marks obtained by the students in physics and in mathematics are as follows.

Marks in Physics	35	23	47	17	10	43	9	6	28
Marks in Mathematics	30	33	45	23	8	49	12	4	31

Compute of correlation of ranks.

Q. Following are the marks of

10

students obtained in Physics and Chemistry in an examination. Find the rank-correlation coefficient.

x	43	96	74	38	35	43	22	56	35	80
y	30	94	84	13	30	18	30	41	48	95

Given below is the percentage of marks secured by 5 students in Economics and Statistics.

$\begin{matrix} Students & A & B & C & D & E Marks in Economics & 60 & 48 & 49 & 50 & 55 Marks in Statistics & 85 & 60 & 55 & 65 & 75 \end{matrix}$
Calculate the coefficient of rank correlation.

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The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.StudentABCDEFGHIJKLHistory693639716776402085655534Mathematics335271257922838124354664

The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.
Student A B C D E F G H I J K L
History 69 36 39 71 67 76 40 20 85 65 55 34
Mathematics 33 52 71 25 79 22 83 81 24 35 46 64