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Statistical Methods in Economics
Notes
⎡ N1 ⎤ ⎛ + ⎞ th
Q 3 = Value of the 3 ⎜ ⎟ ⎥ item
⎢
⎣ ⎝ 4 ⎠ ⎦
⎡ ( + ) 315 1 ⎤ th
th
= ⎢ ⎥ item i.e., 12 item = 66
⎣ 4 ⎦
Q– Q 1 66 – 52 14
3
Q.D. = = = = 7
2 2 2
Q– Q 66 – 52 14
Coefficient of Q.D. = 3 1 = = = 0.118
Q + Q 1 66 + 52 118
3
Q.D. in Discrete Series
Example 9: Calculate quartile deviation and its coefficient from the following data:
Height of students (in cms.) 120 122 124 126 130 140 150 160
No. of students 1 3 5 7 10 3 1 1
Solution:
Calculation of Q and Q 1
3
X f c.f.
120 1 1
122 3 4
124 5 9
126 7 16
130 10 26
140 3 29
150 1 30
160 1 31
Q 1 = Size of ⎛ ⎜ N1 ⎞ + ⎟ th item = 8 th item
⎝ 4 ⎠
∴ Q 1 = 224.
Q 3 = Size of 3 ⎛ ⎜ N1 ⎞ + ⎟ th item = 24 th item
⎝ 4 ⎠
∴ Q 3 = 230
Q– Q
Q.D. = 3 1
2
230 – 224
= = 3 cms.
2
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