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Calculate Q.D. of the following data: Height of plants (in feet) 2 – 4 4 – 6 6 – 8 8 – 10 10 –12 14 – 14 14 – 16 No. of plants 15 20 25 12 18 13 17 - Mathematics and Statistics

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Sum

Calculate Q.D. of the following data:

Height of plants (in feet) 2 – 4 4 – 6 6 – 8 8 – 10 10 – 12 14 – 14 14 – 16
No. of plants 15 20 25 12 18 13 17
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Solution

We construct the less than cumulative frequency table as follows:

Height of plants (in feet) No. of plants
(f)
Less than cumulative frequency
(c.f.)
2 – 4 15 15
4 – 6 20 35 ← Q1
6 – 8 25 60
8 – 10 12 72
10 – 12 18 90 ← Q3
12 – 14 13 103
14 – 16 17 120
Total N = 120  

Here, N = 120

Q1 class = class containing `("N"/4)^"th"` observation

∴ `"N"/4 = 120/4` = 30
Cumulative frequency which is just greater than (or equal to) 30 is 35.
∴ Q1 lies in the class 4 – 6
∴ L = 4, c.f. = 15, f = 20, h = 2

∴ Q1 = `"L" + "h"/"f"("N"/4 - "c.f.")`

= `4 + 2/20 (30 - 15)`

= `4 + 1/10 xx 15`

= 4 + 1.5
= 5.5

Q3 class = class containing `((3"N")/4)^"th"` observation

∴ `(3"N")/4 = (3 xx 120)/4` = 90
Cumulative frequency which is just greater than (or equal to) 90 is 90.
∴ Q3 lies in the class 10 – 12
∴ L = 10, c.f. = 72, f = 18, h = 2

∴ Q3 = `"L" + "h"/"f"((3"N")/4 - "c.f.")`

= `10 + 2/18 (90 - 72)`

= `10 + 2/18 xx 18`

= 10 + 2
∴ Q3 = 12

∴ Q.D. = `("Q"_3 - "Q"_1)/2`

= `(12 - 5.5)/2`

= `(6.5)/2`

= 3.25

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

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 2 Measures of Dispersion
Miscellaneous Exercise 2 | Q 7 | Page 35
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