the rank correlation coefficient of the following data
Answers
Step-by-step explanation:
Considering this case we are taking a problem and try to solve it. Example 3: Calculate rank correlation coefficient from the following data:.
Answer :0.6303
Step-by-step explanation: Let the ranks of students obtained in Physics be x and the ranks of students obtained in Chemistry be y.
X Y Rank X
(x) Rank Y
(y) d=x−y d
2
43 30 5.5 7 −1.5 2.25
96 94 1 2 −1 1
74 84 3 3 0 0
38 13 7 10 −3 9
35 30 8.5 7 1.5 2.25
43 18 5.5 9 −3.5 12.25
22 30 10 7 3 9
56 41 4 5 −1 1
35 48 8.5 4 4.5 20.25
80 95 2 1 1 1
∑ 0 58
In the X series 43 has repeated twice and given ranks 5.5 instead of 5 and 6.
For this the correction factor is
12
2(4−1)
=
2
1
.
Also 35 has repeated twice and given ranks 8.5 instead of 8 and 9. For this the correction factor is
12
2(4−1)
=
2
1
.
In the Y series 30 has repeated thrice and given ranks 7 instead of 6,7,8.
For this the correction factor is
12
3(9−1)
=2.
So, the total correction factors C.F=
2
1
+
2
1
+2=3
The rank correlation coefficient is given by,
r=1−
n(n
2
−1)
6(∑d
2
−C.F)
=1−
10(100−1)
6(58+3)
=1−
10×99
276
=1−
990
366
=1−0.3696
=0.6303
Therefore the rank correlation coefficient is 0.6303.