The mean and the median of the following ten numbers in increasing...

Since, number of observations are even $n = 10$

Hence, the median is $= \dfrac{{\left(\dfrac{n}{2}\right)}^{th}term + {\left(\dfrac{n}{2} + 1\right)}^{th}term}{2} = \dfrac{{5}^{th}term + {6}^{th}term}{2}$

Thus, median $= \dfrac{34 + x}{2}$

$⇒ \dfrac{34 + x}{2} = 35$

$⇒ x = 36 . . . \left(i\right)$

And, mean$= \dfrac{sumofterms}{numberofterms}$

$⇒ \dfrac{10 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + y}{10} = 42$

$⇒ x + y + 300 = 420$

$⇒ x + y = 120 . . . \left(ii\right)</p><p>Put$ the value ofx from \left(i\right) in $\left(ii\right),$ to get

$36 + y = 120$

$⇒ y = 84$

⇒ \dfrac{y}{x} = \dfrac{84}{36} = \dfrac{7}{3} .