91Ó°ÊÓ

We are given that standard deviations are $6$and we have to find out the percentage of observations in any data set that lie in it.

The Chebyshev's rule state that the percentage of the observation lie with in x standard deviation is given by, $(1-\frac{1}{x^2})×100$

where x is no of standard deviations.

and we are given that $x=6$.

Putting the value in formula,

we get, $(1-\frac{1}{6^2})×100=(1-\frac{1}{36})×100$

On solving we get $97.2\%$.

Hence,$97.2\%$of observations lie with in the$6$standard deviations.

We are given that standard deviations are $1.5$and we have to find out the percentage of observations in any data set that lie in it.

The Chebyshev's rule state that the percentage of the observation lie with in x standard deviation is given by, $(1-\frac{1}{x^2})×100$

where x is no of standard deviations.

and we are given that $x=1.5$.

Putting the value in formula,

we get,$(1-\frac{1}{1.5^2})×100=(1-\frac{1}{2.25})×100$

On solving we get$55.55\%$.

Hence, $55.55\%$of observations lie with in the $1.5$standard deviations.