Let x _ 1 , x _ 2 , x _ 3 .... x _ k be k observations and w _ i = a x _ i + b for i = 1,2, 3..... k , where a and b are constants. If mean of x _ i is 52 and their standard deviation is 12 and mean of w _ i is 60 and

Correct answer: A. a = 1.25, b = - 5 w _ i = a x _ i + b ⇒ ¯ w = a ¯ x + b ⇒ 60 = a (52) + b …. (i) S. Dofw = |a|(S. Dof x _ i ) 15 = |a|12 ⇒ a = ±1.25 …. (ii) From (i) and (ii), we get, If a = 1.25 ⇒ 60 = 65 + b ⇒ b = - 5 If a = - 1.25 ⇒ 60 = - 65 + b ⇒ b = 125

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Statistics

NTA Abhyas 2020 · Mathematics · Statistics

Let x _ 1 , x _ 2 , x _ 3 .... x _ k be k observations and w _ i =...

Let

{x}_{1}, {x}_{2}, {x}_{3}.... {x}_{k}

k

observations and

{w}_{i} = a{x}_{i} + b

for

i = 1,2, 3..... k

, where

a

and

b

are constants. If mean of

{x}_{i}

52

and their standard deviation is

12

and mean of

{w}_{i}

60

and their standard deviation is

15

, then the value of

a

and

b

should be

Options

A $a = 1.25, b = - 5$
B $a = - 1.25, b = 5$
C $a = 2.5, b = - 5$
D $a = 2.5, b = 5$

Correct answer

A. $a = 1.25, b = - 5$

Step-by-step solution

${w}_{i} = a{x}_{i} + b$
$⇒ \overset{¯}{w} = a\overset{¯}{x} + b$
$⇒ 60 = a \left(52\right) + b$ …. (i)

$S. Dofw = \left|a\right|\left(S. Dof{x}_{i}\right)$
$15 = \left|a\right|12$
$⇒ a = \pm1.25$ …. (ii) $From (i) and (ii), we get, If$ a = 1.25 ⇒ 60 = 65 + b ⇒ b = - 5 $ If$ a = - 1.25 ⇒ 60 = - 65 + b ⇒ b = 125 $$

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