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4
rd
is called 3 quartile class. Then apply the respective
formulae
N
− m1
Q1 = l1 + 4
× c1
f1 N
3 − m3
4
Q3 = l3 + × c3
f3
Where l1 = lower limit of the first quartile class
f1 = frequency of the first quartile class
c1 = width of the first quartile class
m1 = c.f. preceding the first quartile class
l3 = 1ower limit of the 3rd quartile class
f3 = frequency of the 3rd quartile class
c3 = width of the 3rd quartile class
m3 = c.f. preceding the 3rd quartile class
Example 24:
The following series relates to the marks secured by
students in an examination.
Marks
No. of students
010
11
1020
18
2030
25
3040
28
4050
30
5060
33
6070
22
7080
15
8090
12
90100
10
123 Find the quartiles
Solution :
C.I.
010
1020
2030
3040
4050
5060
6070
7080
8090
90100 Q1 Q3 f
11
18
25
28
30
33
22
15
12
10
204 cf
11
29
54
82
112
145
167
182
194
204 N
N 204 3 = = 51
4
4
4
N
− m1
4
= l1 +
× c1
f1
51 − 29
= 20 +
× 10
= 20 + 8.8 = 28.8
25 N
3 − m3
4
= l3 + × c3
f3
= 60 + = 153 153 − 145
× 12 = 60 +4.36 = 64.36
22 Deciles :
These are the values, which divide the total number of
observation into 10 equal parts. These are 9 deciles D1, D2…D9.
These are all called first decile, second decile…
etc.,
124 Deciles for Raw data or ungrouped data
Example 25:
Compute D5 for the data given below
5, 24, 36, 12, 20, 8
Solution :
Arranging the given values in the increasing order
5, 8, 12, 20, 24, 36
th 5( n + 1) D5 = observation 10 th 5(6 + 1) = observation 10 = (3.5)th observation
1
= 3rd item +
[ 4th item – 3rd item]
2
1
= 12 +
[20 – 12] = 12+ 4 = 16
2
Deciles for Grouped data :
Example 26:
Calculate D3 and D7 for the data given below
Class
Interval 010 Frequency :
Solution : 5 1020 2030 3040 4050 5060 6070
7
C.I
010
1020
2030
3040
4050
5060
6070 12
f
5
7
12
16
10
8
4
62
125 16 10
c.f
5
12
24
40
50
58
62 8 4 th 3N D3 item = item 10 th 3 × 62 = item 10 = (18.6)th item
which lies in the interval 2030
N
3 − m
10
∴ D3 = l + ×c
f
18.6 12
= 20 +
× 10
12
= 20 + 5.5 = 25.5
th 7× N D7 item = item 10 th 7 × 62 = item 10 th 434 th
= item = (43.4) item
10 which lies in the interval(4050) 7N 10 − m D7 = l + ×c
f
43.4 − 40
= 40 +
× 10
10
= 40 + 3.4 = 43.4
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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