Applied Mathematics for Electrical Engineering (3130908)

Question-5c ( i )-OR

BE | Semester-3 Winter-2019 | 26-11-2019

Q5) (c ( i ))

Given observations in ascending order:

4, 6, 8, 10, 10, 12, 14, 16, 18, 20 .

Q_{1} = {(\frac{N + 1}{4})}^{th} observation

Q_{1} = {(\frac{10 + 1}{4})}^{th} observation

Q_{1} = {(\frac{11}{4})}^{th} observation

Q_{1} = 2 . 75^{th} observation

Here,

2^{nd} observation

6

and now add

0.75 * (2^{nd} observation - 3^{rd} observation)

to the

2^{nd} observation .

\Rightarrow 6 + 0.75 * (8 - 6) = 7.5

Therefore,

2 . 75^{th}

observation is

7.5

Q_{3} = {(\frac{3 (N + 1)}{4})}^{th} observation

Q_{1} = {(\frac{3 (10 + 1)}{4})}^{th} observation

Q_{1} = {(\frac{11}{4})}^{th} observation

Q_{1} = 8 . 25^{th} observation

Here,

8^{th} observation

18

and now add

0.25 * (8^{th} observation - 9^{th} observation)

to the

8^{th} observation .

\Rightarrow 18 + 0.25 * (20 - 18) = 18.5

Therefore,

8 . 25^{th}

observation is

18.5

C . D . = \frac{Q_{3} - Q_{1}}{Q_{3} + Q_{1}} = \frac{18.5 - 7.5}{18.5 + 7.5} = 0.4231