"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 < x1 < x2 < x3 < ... < x15 = 10 and $\sum\limits_{i = 1}^{15} {{f_i}}$ > 0, the standard deviation cannot be :"

Accepted Answer

"If variate varries from m to M then variance

${\sigma ^2} \le {1 \over 4}{\left( {M - m} \right)^2}$

(M = upper bound of value of any random variable,

m = Lower bound of value of any random variable)

Here M = 10 and m = 0

$\therefore$ ${\sigma ^2} \le {1 \over 4}{\left( {10 - 0} \right)^2}$

$\Rightarrow$ ${\sigma ^2} \le 25$

$\Rightarrow$ $- 5 \le \sigma \le 5$

$\therefore$ $\sigma$ $\ne$ 6"

For the frequency distribution :
Variate (x) : x₁ x₂ x₃ .... x₁₅
Frequency (f) : f₁ f₂ f₃ ...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and
$\sum\limits_{i = 1}^{15} {{f_i}}$ > 0, the standard deviation cannot be :

Solution

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For the frequency distribution : Variate (x) : x1 x2 x3 .... x15 Frequency (f) : f1 f2 f3 ...... f15 where 0 < x1 < x2 < x3 < ... < x15 = 10 and $\sum\limits_{i = 1}^{15} {{f_i}}$ > 0, the standard deviation cannot be :

Solution

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More Statistics questions

Drill 25 more like these. Every day. Free.

For the frequency distribution :
Variate (x) : x₁ x₂ x₃ .... x₁₅
Frequency (f) : f₁ f₂ f₃ ...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and
$\sum\limits_{i = 1}^{15} {{f_i}}$ > 0, the standard deviation cannot be :