# 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

#### 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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