Maharashtra State BoardHSC Commerce 11th
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Find the Q.D. for the following data.3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3. - Mathematics and Statistics

Sum

Find the Q.D. for the following data.
3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3.

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Solution

The given data can be arranged in ascending order as follows:
3, 3, 5, 5, 8, 9, 11, 15, 16, 17, 19.
Here, n = 11

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

= value of `((11+1)/4)^"th"` observation

= value of 3rd observation
∴ Q1 = 5

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

= value of `3((11 + 1)/4)^"th"` observation
= value of (3 × 3)th observation
= value of 9th observation
∴ Q3 = 16

Q.D. = `("Q"_3-"Q"_1)/(2)`

= `(16 - 5)/(2)`

= `(11)/(2)`
∴ Q.D. = 5.5

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