5 students of a class have an average height 150cm and variance 18c...

Let ${1}^{st}5$ students are

${x}_{1}, {x}_{2}, {x}_{3}, {x}_{4} and {x}_{5}$

$∴ 18 = E$\left({x}^{2}\right) - {\left(E\left(x\right)\right)}^{2}$<br/><br/>$= \dfrac{{x}_{1}^{2} + {x}_{2}^{2} + {x}_{3}^{2} + {x}_{4}^{2} + {x}_{5}^{2}}{5} - {\left(150\right)}^{2}

$⇒ {x}_{1}^{2} + {x}_{2}^{2} + {x}_{3}^{2} + {x}_{4}^{2} + {x}_{5}^{2} = 112590$

$∴$ new variance $= \dfrac{{x}_{1}^{2} + {x}_{2}^{2} + . . . . + {x}_{5}^{2} + {156}^{2}}{6} - {( 151 )}^{2}$\left[Sincenewmean = \dfrac{150 \times 5 + 156}{6} = 151\right]$<br/><br/>$= \dfrac{112590 + 24336}{6} - 22801$<br/><br/>$= 20