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Given below are the prices of shares of a company for the last 10 days. Find Q.D.: 172, 164, 188, 214, 190, 237, 200, 195, 208, 230. - Mathematics and Statistics

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Sum

Given below are the prices of shares of a company for the last 10 days. Find Q.D.: 172, 164, 188, 214, 190, 237, 200, 195, 208, 230.

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Solution

The given data can be arranged in ascending order as follows:
164, 172, 188, 190, 195, 200, 208, 214, 230, 237
Here, n = 10

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

= value of `((10 + 1)/4)^"th"` observation

= value of (2.75)th observation
= value of 2nd observation + 0.75 (value of 3rd observation – value of 2nd observation)
= 172 + 0.75 (188 – 172)
= 172 + 0.75 (16)
= 172 + 12
= 184

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

= value of `3((10 + 1)/4)^"th"` observation

= value of (3 × 2.75)th observation
= value of 8th observation + 0.25 (value of 9th observation – value of 8th observation)
= 214 + 0.25 (230 – 214)
= 214 + 0.25 (16)
= 214 + 4
= 218

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

= `(218 - 184)/(2)`

= `(34)/(2)`
= 17

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