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Unformatted text preview: d the third quartile of a distribution. When a distribution is divided into four
equal parts, we obtain four quartiles, Q1, Q2, Q3 and Q4.
First quartile Q1 is point of the distribution where 25% of the items of the
distribution lie below Q1, and 75% of the items of the distribution lie above
the Q1. Q2 is the median of the distribution, where 50% of the items of the
distribution lie below Q2, and 50% of the items of the distribution lie above
the Q2. Third quartile Q3 is point of the distribution where 75% of the items of
the distribution lie below Q3, and 25% of the items of the distribution lie
above the Q3.
Quartile deviation is based on the difference between the third and first
quartiles. So quartile deviation is defined as the interquartile range.
Symbolically, interquartile range = Q3 Q1 Quartile Deviation = (Q3 Q1) / 2 Coefficient of Quartile Deviation = (Q3 Q1) / (Q3 + Q1) Sikkim Manipal University Page No. 188 Research Methodology Unit 11 Merits of Quartile Deviation
1. Quartile Deviation is superior to range as a rough measure of
dispersion.
2. It has a special merit in measuring dispersion in openended series.
3. Quartile Deviation is not affected by extreme values.
Demerits of Quartile Deviation
1. Quartile Deviation ignores the first 25% of the distribution below Q1 and
25% of the distribution above the Q3.
2. Quartile Deviation is not amenable to further mathematical treatment.
3. Quartile Deviation is very much affected by sampling fluctuations.
Problems
Individual Series
1. Find the Quartile Deviation and its coefficient.
20 58 40 12 30 15 50 First of all arrange the data according to ascending order.
12
Q1 15 20 28 30 40
th Size of (N+1) / 4 = Size of (7+1) / 4 th item = Size of (8 / 4) th item = 2nd item = 15 = Size of 3(N+1) / 4 th item = Size of 3 X (7+1) / 4 th item = Size of 3 X 8 / 4 th item = (3 X 2) nd item = 6th item = Q3 = 50 40 Sikkim Manipal University item Page No. 189 Research Methodology Unit 11 Coefficient of Quartile Deviation = (Q3 Q1) / (Q3 + Q1) = (40 15) / (40+ 15) = 25/55 = .4545 Discrete Series
2. Find quartile Deviat...
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This note was uploaded on 04/15/2010 for the course MBA mba taught by Professor Smu during the Spring '10 term at Manipal University.
 Spring '10
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