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Unformatted text preview: widely
used.
Demerits:
1. It is very much affected by the extreme items.
2. It is based on only two extreme observations.
3. It cannot be calculated from openend class intervals.
4. It is not suitable for mathematical treatment.
5. It is a very rarely used measure.
7.4 Quartile Deviation and Co efficient of Quartile
Deviation :
7.4.1 Quartile Deviation ( Q.D) :
Definition: Quartile Deviation is half of the difference
between the first and third quartiles. Hence, it is called Semi
Inter Quartile Range.
Q − Q1
In Symbols, Q . D = 3
. Among the quartiles Q1, Q2
2
and Q3, the range Q3 − Q1 is called inter quartile range and
Q 3 − Q1
, Semi inter quartile range.
2
144 7.4.2 Coefficient of Quartile Deviation :
Q 3 − Q1
Coefficient of Q.D =
Q 3 + Q1
Example 3:
Find the Quartile Deviation for the following data:
391, 384, 591, 407, 672, 522, 777, 733, 1490, 2488
Solution:
Arrange the given values in ascending order.
384, 391, 407, 522, 591, 672, 733, 777, 1490, 2488.
n +1
10 + 1
Position of Q1 is
=
= 2.75th item
4
4
Q1 = 2nd value + 0.75 (3rd value – 2nd value )
= 391 + 0.75 (407 – 391)
= 391 + 0.75 × 16
= 391 + 12
= 403
n +1
Position Q3 is 3
= 3 × 2.75 = 8.25th item
4
Q3 = 8th value + 0.25 (9th value – 8th value)
= 777 + 0.25 (1490 – 777)
= 777 + 0.25 (713)
= 777 + 178.25 = 955.25
Q − Q1
Q.D = 3
2
955.25 − 403
=
2
552.25
=
= 276.125
2
Example 4 :
Weekly wages of labours are given below. Calculated Q.D and
Coefficient of Q.D.
Weekly Wage (Rs.) :100 200
400
500
600
No. of Weeks
:5
8
21
12
6
145 Solution :
Weekly
Wage (Rs.)
100
200
400
500
600
Total No. of Weeks
5
8
21
12
6
N=52 Cum. No. of
Weeks
5
13
34
46
52 N + 1 52 + 1
=
= 13.25th item
4
4
Q1
= 13th value + 0.25 (14th Value – 13th value)
= 13th value + 0.25 (400 – 200)
= 200 + 0.25 (400 – 200)
= 200 + 0.25 (200)
= 200 + 50 = 250 N +1
th
Position of Q3 is 3 = 3 × 13.25 = 39.75 item
4
Q3
= 39th value + 0.75 (40th value – 39th value)
= 500 + 0.75 (500 – 500)
= 500 + 0.75 ×0
= 500
Q 3 − Q...
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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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