For the frequency distribution: Variate (x): x1 x2 x3 ...x15 Frequency (f): f1 f2 f3...f15 where 0

Question

For the frequency distribution: Variate (x): x1 x2 x3 ...x15 Frequency (f): f1 f2 f3...f15 where 0< x 1< x 2< x 3< ldots< x 15=10 and displaystyle∑i=115 fi>0, the standard deviation cannot be : (A) 2 (B) 1 (C) 4 (D) 6

Tardigrade Admin · Accepted Answer

∵ σ2 ≤ (1/4)( M - m )2 Where M and m are upper and lower bounds of values of any random variable. ∴ σ2 < (1/4)(10-0)2 ⇒ 0 < σ < 5 ∴ σ ≠ 6.

Variate (x) :	$x_{1}$	$x_{2}$	$x_{3} ... x_{15}$
Frequency (f) :	$f_{1}$	$f_{2}$	$f_{3} ... f_{15}$

Q. For the frequency distribution :

Variate (x) : $x_{1}$ $x_{2}$ $x_{3} ... x_{15}$

Frequency (f) : $f_{1}$ $f_{2}$ $f_{3} ... f_{15}$

where $0 < x_{1} < x_{2} < x_{3} < \dots < x_{15} = 10$ and $i = 1 \sum 15 f_{i} > 0,$ the standard deviation cannot be :

2

1

4

6

$∵ σ^{2} \leq \frac{1}{4} (M - m)^{2}$
Where $M$ and $m$ are upper and lower bounds
of values of any random variable.
$∴ σ^{2} < \frac{1}{4} (10 - 0)^{2}$
$\Rightarrow 0 < σ < 5$
$∴ σ \neq = 6$ .

Q. For the frequency distribution : Variate (x) : x1​ x2​ x3​...x15​ Frequency (f) : f1​ f2​ f3​...f15​ where 0<x1​<x2​<x3​<…<x15​=10 and i=1∑15​fi​>0, the standard deviation cannot be :

2

1

4

6

∵σ2≤41​(M−m)2 Where M and m are upper and lower bounds of values of any random variable. ∴σ2<41​(10−0)2 ⇒0<σ<5 ∴σ=6.

Q. For the frequency distribution :

Variate (x) : $x_{1}$ $x_{2}$ $x_{3} ... x_{15}$

Frequency (f) : $f_{1}$ $f_{2}$ $f_{3} ... f_{15}$

where $0 < x_{1} < x_{2} < x_{3} < \dots < x_{15} = 10$ and $i = 1 \sum 15 f_{i} > 0,$ the standard deviation cannot be :

$∵ σ^{2} \leq \frac{1}{4} (M - m)^{2}$
Where $M$ and $m$ are upper and lower bounds
of values of any random variable.
$∴ σ^{2} < \frac{1}{4} (10 - 0)^{2}$
$\Rightarrow 0 < σ < 5$
$∴ σ \neq = 6$ .