For the frequency distribution : Variate (x) : x1 x2 x3 ....

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

Solutions · 1