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 < … < x 15 = 10 and ∑ i = 1 15 f i > 0 , the standard deviation cannot be

Step-by-step solution

We know σ 2 ≤ 1 4 M - m 2 . Where M is upper bound of value of any random variable and m is lower bound of any random variable, ⇒ σ 2 ≤ 1 4 10 - 0 2 ⇒ σ 2 < 25 , (removed equality sign because m > 0 ) ⇒ - 5 < σ < 5 From given options σ ≠ 6 .