Find Rank Correlation Coefficient 






Solution 


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Find Rank Correlation Coefficient

1. Ten participants in a contest are ranked by two judges as follows
x 
1 
6 
5 
10 
3 
2 
4 
9 
7 
8 
f 
6 
4 
9 
8 
1 
2 
3 
10 
5 
7 
Calculate the rank correlation coefficient.
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2. The values of the same 15 student in two subject A and B are given below
the two numbers within the brackets denoting the ranks of the same student in A and B respectively.
(1,10), (2,7), (3,2), (4,6), (5,4), (6,8), (7,3), (8,1), (9,11),(10,15), (11,9), (12, 5), (13, 14), (14,12), (15, 13). Find the rank correlation coefficient.
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3. The rank of the same 16 students in statistics and biology are as follows. Brackets represent the rank of the students in Statistics and Biology.
(1,1), (2,10), (3,3),(4,4), (5,5), (6,7), (7,2), (8,6), (9,8), (10,11), (11,15), (12, 9), (13, 14), (14,12), (15,16), (16, 13). Find the rank correlation coefficient.
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4. Ten competitors in a musical test were ranked by the three judges A, B andC in the following order:
judge A 
1 
6 
5 
10 
3 
2 
4 
9 
7 
8 
judge B 
3 
5 
8 
4 
7 
10 
2 
1 
6 
9 
judge C 
6 
4 
9 
8 
1 
2 
3 
10 
5 
7 
Using rank correlation method. Discuss which pair of judges has the nearest approach to common liking in music.
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5. Calculate the coefficient of rank correlation from the following data
x 
60 
34 
40 
50 
45 
41 
22 
43 
42 
66 
64 
46 
f 
75 
32 
34 
40 
45 
33 
12 
30 
36 
72 
41 
57 
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6. Obtain the rank correlation coefficient for the following data.
X 
68 
64 
75 
50 
64 
80 
75 
40 
55 
64 
Y 
62 
58 
68 
45 
81 
60 
68 
48 
50 
70 
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7. Obtain the rank correlation coefficient for the following data.
X 
48 
33 
40 
9 
16 
16 
65 
24 
16 
57 
Y 
13 
13 
24 
6 
15 
4 
20 
9 
6 
19 
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Find Rank Correlation Coefficient

1. Calculate Rank Correlation Coefficient from the follwing data
X  Y  Rx  Ry  d = Rx  Ry  d^{2}  35  102  10  1  9  81  40  101  8.5  2.5  6  36  42  97  6  5.5  0.5  0.25  43  98  5  4  1  1  40  38  8.5  10  1.5  2.25  53  101  3  2.5  0.5  0.25  54  97  2  5.5  3.5  12.25  49  92  4  9  5  25  41  95  7  7.5  0.5  0.25  55  95  1  7.5  6.5  42.25                        200.5 
`r = 1  (6 * sum d^2)/(n(n^2  1))`
` = 1  (6 * 200.5)/(10 * (10^2  1))`
` = 1  (6 * 200.5)/(10 * (100  1))`
` = 1  1203/990`
` = (990  1203)/990`
` = 213/990`
` = 0.2152`




