In an entrance examination, for admission to the engineering course of a certain university, the top 50 students, who were selected, got the following percentage of marks in the aggregate:
|
95 92 |
91 |
90 |
88 |
82 |
86 87 |
|
87 88 |
70 |
72 |
76 |
77 |
77 79 |
|
79 79 |
78 |
78 |
68 |
67 |
67 66 |
|
65 63 |
63 |
63 |
63 |
64 |
58 59 |
|
60 60 |
60 |
60 |
61 |
62 |
62 62 |
S = smallest) = 95 % - 50% = 45%
|
Marks |
No. of Students |
|
0 – 10 |
8 |
|
10 – 20 |
40 – 8 = 32 |
|
20 – 30 |
80 – 40 = 40 |
|
30 – 40 |
96 – 80 = 16 |
|
40 – 50 |
100 – 96 = 4/p |
|
55 |
55 |
56 |
57 |
54 |
53 |
52 |
|
|
55 |
50 |
(i) Obtain the range of the distribution of percentage of marks.
(ii) Classify the data in class intervals as(a) 45 – 55,55 – 65,65 – 75, ...........
(b) 50 – 55, 55 – 60, 60 – 65, ...........
(iii) Examine the error of grouping in each case.
(ii)(a)
|
C. I. |
Tally Bars |
fx |
|
45 – 55 |
|
5 |
|
55 – 65 |
|
20 |
|
65 – 75 |
|
7 |
|
75 – 85 |
|
9 |
|
85 – 95 |
|
1 8 |
|
95 – 105 |
|
1 |
|
50 |
(b)
|
C.I. |
Tally Bars |
fx |
|
50 – 55 |
|
5 |
|
55 – 60 |
|
7 |
|
60 – 65 |
|
13 |
|
65 – 70 |
|
5 |
|
70 – 75 |
|
2 |
|
75 – 80 |
|
8 |
|
85 – 85 |
|
1 |
|
85 – 90 |
|
5 |
|
90 – 95 |
|
3 |
|
95 – 100 |
|
1 |
|
50 |
(iii) Error of grouping as per (ii) (a)
|
C. I. |
A. Value |
M |
(A.V. – M) Σ of Group |
|
45 – 55 |
54, 53, 52, 50 |
|
4, 3, 2, 2, 0 |
|
55 – 65 |
63, 58 |
||
|
65 – 75 |
70, 68, 72, 67, 67, 66, 65 |
|
0, –2, 2, –3, –3, –4, –5 |
|
75 – 85 |
79, 72, 79, 76, 77, 78, 77, 78 |
|
–1, –8, –1, –4, –1, –3 |
|
85 – 95 |
88, 86, 92, 87, 91, 90, 87, 88 |
|
–2, –4, 2, –3, 1, 0, –3, –2 |
|
95 – 105 |
95 |
|
–5 |
