# 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

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

#### 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