This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 1
500 − 250 250
Q.D. =
=
=
= 125
2
2
2
Q − Q1
Coefficient of Q.D. = 3
Q 3 + Q1
500 − 250
=
500 + 250
250
=
= 0.3333
750
Position of Q1 in 146 Example 5:
For the date given below, give the quartile deviation and
coefficient of quartile deviation.
X : 351 – 500 501 – 650 651 – 800 801–950 951–1100
f:
48
189
88
4
28
Solution :
x
351 500
501 650
651 800
801 950
951 1100
Total f
48
189
88
47
28
N = 400 True class
Intervals
350.5 500.5
500.5 650.5
650.5 800.5
800.5 950.5
950.5 1100.5 N
− m1
Q1 = l1 + 4
× c1
f1
N
400
=
= 100,
4
4
Q1 Class is 500.5 – 650.5
l1 = 500.5, m1 = 48, f1 = 189, c1 = 150
100 − 48
× 150
∴ Q1 = 500.5 +
189
52 × 150
= 500.5 +
189
= 500.5 + 41.27
= 541.77
N
3
− m3
4
Q3 = l3 +
× c3
f3
147 Cumulative
frequency
48
237
325
372
400 N
= 3 × 100 = 300,
4
Q3 Class is 650.5 – 800.5
l3 = 650.5, m3 = 237, f3 = 88, C3 = 150
300  237
× 150
∴ Q3 = 650.5 +
88
63 × 150
= 650.5 +
88
= 650.5 + 107.39
= 757. 89
Q − Q1
∴ Q.D = 3
2
757.89 − 541 .77
=
2
216.12
=
2
= 108.06
Q − Q1
Coefficient of Q.D = 3
Q 3 + Q1
757.89 − 541.77
=
757.89 + 541.77
216.12
=
= 0.1663
1299.66
7.4.3 Merits and Demerits of Quartile Deviation
Merits :
1. It is Simple to understand and easy to calculate
2. It is not affected by extreme values.
3. It can be calculated for data with open end classes also.
Demerits:
1. It is not based on all the items. It is based on two
positional values Q1 and Q3 and ignores the extreme
50% of the items
3 148 2. It is not amenable to further mathematical treatment.
3. It is affected by sampling fluctuations.
7.5 Mean Deviation and Coefficient of Mean Deviation:
7.5.1 Mean Deviation:
The range and quartile deviation are not based on all
observations. They are positional measures of dispersion. They
do not show any scatter of the observations from an average.
The mean deviation is measure of dispersion based on all
items in a distribution.
Definition:
Mean deviation is the arithmetic mean of the deviations
of a seri...
View
Full
Document
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

Click to edit the document details