4. Ten students obtained the following percentage of
marks in the college internal test (x) and in the
final university examination (y). Find the
correlation coefficient between the marks of the
two test.
X
51 63 63 49 50 60 65 63 46 50
y 49 72 75 50 48 60 70 48 60 56
Answers
Step-by-step explanation:
ANSWER
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
Answer:
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Step-by-step explanation:
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