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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.

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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

Q_{1} = value of `(("n" + 1)/4)^"th"` observation

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

= value of (2.75)^{th} observation

= value of 2^{nd} observation + 0.75 (value of 3^{rd }observation – value of 2^{nd} observation)

= 172 + 0.75 (188 – 172)

= 172 + 0.75 (16)

= 172 + 12

= 184

Q_{3} = 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 8^{th} observation + 0.25 (value of 9^{th }observation – value of 8^{th} 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

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