(a) Find the rank or Spearman correlation coefficient between the midterm grade and the IQ ranking of a random sample of 10 students in a large class, as given in Table, using Eq.
(a) When is the rank correlation used?
Table Midterm Grade and IQ Ranking
|
Student
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Midterm grade
|
77
|
78
|
65
|
84
|
84
|
88
|
67
|
92
|
68
|
96
|
|
IQ ranking
|
7
|
6
|
8
|
5
|
4
|
3
|
9
|
1
|
10
|
2
|
Table Calculations to Find the Coefficient of Rank Correlation
|
n
|
Midterm Grade
|
Ranking on Midterm
|
IQ
Ranking
|
D
|
D2
|
|
1
|
96
|
1
|
2
|
-1
|
1
|
|
2
|
92
|
2
|
1
|
1
|
1
|
|
3
|
88
|
3
|
3
|
0
|
0
|
|
4
|
84
|
4.5
|
4
|
0:5
|
0.25
|
|
5
|
84
|
4.5
|
5
|
-0:5
|
0.25
|
|
6
|
78
|
6
|
6
|
0
|
0
|
|
7
|
77
|
7
|
7
|
0
|
0
|
|
8
|
68
|
8
|
10
|
-2
|
4
|
|
9
|
67
|
9
|
9
|
0
|
0
|
|
10
|
65
|
10
|
8
|
2
|
4
|
|
P D2 = 10:50
|