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Based on a selective research over a sample of 60 students I have registered the high-school average and the admission score for each student.
The values of the registered variables are presented in Table 1.
Table 1.
Current No High School Average (xi) Admission Score (yi)
1 9 51
2 9.54 60
3 9.25 43
4 9.27 60
5 9.25 55
6 9.21 63
7 8.67 51
8 8.62 37
9 9.44 65
10 9.08 65
11 8.56 53
12 8.23 41
13 8.85 51
14 8.51 59
15 9.24 41
16 8.43 33
17 7.96 48
18 9.73 44
19 9.59 58
20 9.35 36
21 8.97 52
22 9.41 49
23 8.63 47
24 9.99 49
25 6.8 39
26 9.55 52
27 8.56 47
28 8.42 42
29 9.3 51
30 9.22 40
31 8.57 54
32 9.75 63
33 9.32 51
34 8.93 43
35 9.33 46
36 8.91 42
37 9.64 49
38 9.9 56
39 9.47 47
40 9.46 42
41 7.54 39
42 8 46
43 7.4 55
44 8.74 41
45 9.57 45
46 9.27 43
47 8.59 45
48 9.07 55
49 9.19 44
50 8.21 42
51 9.51 57
52 8.95 62
53 9.37 56
54 8.73 42
55 7.72 46
56 9.36 50
57 9.53 62
58 9.76 59
59 8.75 44
60 9.67 46
*Source: Taken from ASE database
1. Compute the average values and of the 60 values
The average HSA mark is:
The average admission score is:
In average each of the 60 students has a high-school average of 8.98 and an admission score of 49.2.
2. Group the 60 values according to each characteristic on 5 equal intervals and present the one-dimensional distributions obatained in the form of tables and statistical graphs
2.a. The HSA mean
We consider the high-school average a variable, the one-dimensional interval distribution obtained after an operation of centralization being presented in Table 2.
Table 2.
Intervals (xi) No. of candidates (ni) (xi) xini
6,79 - 7,42 4 7,105 28,420
7,42 - 8,05 2 7,735 15,470
8,05 - 8,68 14 8,365 117,110
8,68 - 9,31 21 8,995 188,895
9,31 - 9,94 19 9,625 182,875
∑ 60 532,770
*Note: Upper limit of the interval included
*Source: Taken from Table 1.
Computing the Absolute Range
Rx= X - X
Rx= 9.99 – 6.8
Rx= 3.19
Establishing the Number of intervals
r = 5
Determining the width of each interval
k=
k=
k= 0,628 k 0,63
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