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Unit 6: Dispersion: Meaning and Characteristics, Absolute and Relative Measures of Dispersion including Range...

Notes
Q– Q
Coefficient of Q.D. = 3 1
Q + Q 1
3
230 – 224
= = 0.01321.
+
230 224
Answer: Q.D. for the above data is found to be 3 cms. and coefficient of Q.D. = 0.01321.
Q.D. in Continuous Series
Example 10: Find quartile deviation and its relative measure:

Variable Frequency Variable Frequency
20—29 306 50—59 96
30—39 182 60—69 42
40—49 144 70—79 32

Solution:
Calculation OF Q.D.

Variable f c.f.
20—29 306 306
30—39 182 488
40—49 144 632
50—59 96 728
60—69 42 770
70—79 34 804

⎛ 805 ⎞ th
Q = ⎜ 1 ⎟ item = 201.25 th item
⎝ 4 ⎠
which lies in class 20—29 or class 19.5 – 29.5

⎞
Q 1 = 19.5 + ⎛ ⎜ 10 × 201 = 26.07
⎟
⎝ 306 ⎠
( ) 3805 th
th
Q = 4 item = 603.75 item.
3
which lies in 40—49 class or 39.5 — 49.5.
⎞
Q = 39.5 + ⎛ ⎜ 10 + 155 = 47.49
⎟
⎝ 3 144 ⎠
Q– Q
Q.D. = 3 1
2
47.49 – 26.07
= = 10.71
2

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