Maharashtra State BoardHSC Commerce 11th
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Calculate Q. D. for the following data: X 24 25 26 27 28 29 30 F 6 5 3 2 4 7 3 - Mathematics and Statistics

Sum

Calculate Q. D. for the following data:

X 24 25 26 27 28 29 30
F 6 5 3 2 4 7 3
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Solution

X F c.f.
(less than type)
24 6 6
25 5 11 ← Q1
26 3 14
27 2 16
28 4 20
29 7

27 ← Q3

30 3 30
Total 30  

Here, N = 30

Q1 = value of `(("N" + 1)/4)^"th"` observation

= value of `((30 + 1)/4)^"th"` observation

= value of (7.75)th observation

Cumulative frequency which is just greater than (or equal to) 7.75 is 11.
∴ Q1 = 25

Q3 = value of `[3(("n" + 1)/4)]^"th"` observation

= value of `[3((30 + 1)/4)]^"th"` observation

= value of (3 × 7.75)th observation
= value of (23.25)th observation

Cumulative frequency which is just greater than (or equal to) 23.25 is 27.
∴ Q3 = 29

∴ Q.D. = `("Q"_3 - "Q"_1)/(2)`

=  `(29 - 25)/(2)`

= `(4)/(2)`
∴ Q.D. = 2

Concept: Measures of Dispersion - Quartile Deviation (Semi - Inter Quartile Range)
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