Question: 1. Calculate the coefficient of correlation between x and y for the following data:
x
5
4
6
7
8
9
y
8
6
2
3
10
10
4
9
Question: 2. Find the Karl Pearson’s correlation coefficient between the marks in
geography and civics obtained by 8 students
Marks in geography 11 26 14 26 23 12 13 26
Marks in civics
13 23 17 16 19 19 18 24
Question: 3. The following calculations were made in order to find the correlation
coefficient between two variables x and y from 20 pairs of observations:
x 50 ,
y 15 ,
x2
870 ,
y2
485 ,
xy
534
On verification it was found that the pair (x=15,y=9) was copied wrongly, the correct
values being (x=20,y=24). Find the correct value of correlation coefficient.
Question: 4. Calculate Spearman’s correlation coefficient for the following data:
x
52
59
51
50
63
65
y
71
73
70
81
69
84
Question: 5. Find the Spearman’s rank correlation coefficient of the following data:
Series x 100 99
Series y
20
120
98
99
91
93
40
50
60
20
20
30
Question: 6. For the following data:
x
3
5
7
9
10
y
10
14
17
19
20
Calculate the Karl Pearson’s coefficient of correlation between the values of x and y.
Question: 7. Calculate the coefficient of correlation between the heights of mothers and
heights of daughters from the following data:
Heights of mothers(in cm)
70 60 65 67 63
Heights of daughters( in cm)
65 62 60 72 66
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Question: 8. For the following points of observations ( x,y) :
(2,5), (4,4), (5,7), (6,6), (7,8), (9,11)
Calculate Karl Pearson’s coefficient of correlation between the values of x and y.
Question: 9. Find out the Karl Pearson’s coefficient of correlation between the values of x
and y for the following data:
n=50,
x 105 ,
y 120 ,
x2
350 ,
y2
340 ,
xy
320
Question: 10. In a dance competition the judges gave the five competitors the following
marks:
A
B
C
D
E
1st judge 6.5
6.6
6.8
6.4
6.3
2nd judge 7.1
7.2
6.9 6.8
7.3
Find the coefficient of rank correlation.
Question: 11. Ten candidates gave a selection test for entrance in a certain course. At the
end of the course, they were given a proficiency test. The marks secured by candidates in
selection test (x) and proficiency test(y) are given:
Test(x)
12
10
11
15
16
14
Test(y)
20
25
24
23
22
26
Find out the coefficient of correlation by rank.
Question: 12. A mentor while calculating the coefficient of correlation between x and y
from 20 pair of observations got the following results:
n=20,
x 80 ,
y 50 ,
x2
550 ,
y2
360 ,
xy
404
On verification it was found that he had copied down two pairs as (x=4,y=12)
and(x=6,y=4) while the correct values were (x=6,y=10) and(x=4,y=6).Obtain the correct
value of correlation coefficient.
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Question: 13. The marks given to five contestants by three different judges are given as:
Contestants
A
B
C
D
E
Judge x
2
3
1
6
5
Judge y
9
2
1
5
4
Judge z
10
9
8
7
4
Calculate the coefficient of correlation by ranks for each pair of judges.
Question: 14. For the following points of observation(x,y):
(4,8), (6,9), (8,6), (7,4), (10,3), (12,2), (3,1), (2,5), (9,7), (11,10)
Calculate Karl Pearson’s coefficient of correlation between the values of x and y. Also
interpret the result.
Question: 15. The marks in English(x) and science(y) of 12 students in a class are given:
x
71 38 41 73 69 78 42 22 87 67 57 36
y
35 54 73 27 81 24 85 83 26 37 48 66
Calculate the rank correlation coefficient and interpret the result.
Question: 16. The rainfall and the output of maize are as follows:
Rainfall(in cm)
25
40
37
45
48
50
35
32
Maize production 130 160 150 110 130 140 120 140
(in quintals)
Find the correlation coefficient between rainfall and maize production.
Question: 17. From the following data:
Year
No. of vehicles (in millions) No. of casualties (in thousands)
200
3.5
148
2001 4.2
150
2002 3.7
160
2003 4.1
158
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2004 2.5
162
2005 4.8
155
2006 5.5
145
2007 6.5
137
2008 6.1
132
2009 6.2
146
Calculate the rank correlation coefficient between the corresponding number of vehicles
and the number of casualties.
Question: 18. For the following data:
x
21
22
25
26
28
?
y
18
16
14
15
17
19
It is given x 23 , find the missing value of x. Then, find the Karl Pearson’s coefficient of
correlation between the values of x and y.
Question: 19. For the following data:
n=80,
x 90 ,
y
70 ,
x2
210 ,
y2
250 ,
xy
220
Find the Karl Pearson’s coefficient of correlation between the values of x and y.
Question: 20. The following table gives the height of 5 athletes and their measurement of
long jump and high jump to nearest cm.
Height
long jump
high jump
150
302
170
152
310
175
165
350
180
168
350
176
172
380
174
Find the rank correlation coefficient between height and long jump and between height and
high jump. Also comment on the result.
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Answers:
A1. 0.22
A2. 0.61
A3. 0.87
A4.0.086
A5.0.30
A6. 0.99
A7. 0.39
A8. 0.88
A9. 0.83
A10. -0.3
A11. -0.37
A12. 0.98
A13. Correlation between the marks of judges x and y i.e. rxy=0.4 , rxz= -0.6, ryz=0.2
A14. 0.064, negligible relationship
A15. r= -0.76, negative correlation of high order. This means a very good student in
English is very poor in science and vice-versa.
A16. -0.0525
A17. -0.81
A18. -0.67
A19. 0.99
A20. Rank correlation coefficient between height and long jump is 0.95 and between height
and high jump is 0.3 , there is a high relationship between height and long jump and slight
relationship between height and high jump.
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