Question

The coefficient of range of the data set $\{3,1,4,2,5,9,8\}$ can be represented as $\frac{p}{q}$ where $p$ and $q$ are co-primes. Then the value of $(q-p{)}^2$ is:

Answer 1

Given Dataset $\{3,1,4,2,5,9,8\}$

Here

(H) high value $=9$

(L) Low value $=1$

Know

We Range $=H-L$

$=9-1$

$=8$

and

Coefficient of the range $=\frac{H-L}{H+L}$

$=\frac{9-1}{9+1}$

Common factor $=1$

$=\frac{8}{10}$

$\therefore P=4,q=5$

$=\frac{4}{5}$ it is solution of $\frac{p}{q}$

then p and q are coprimes

$\therefore$ value of $(q-p{)}^2=(5-4{)}^2=1^2=1$.