Question

The average height of 10 girls is 158
cm. If one girl's height is neglected,
the average height is increased by 1
cm. Find the height of the
neglected boy *​

Answer 1

$\huge{\mathtt{\purple{Solution\:⇢}}}$

${\underline{\mathtt{\green{GIVEN⇢}}}}$

$\mathtt{⇢\: Average\:height \: of \: 10 \: girls \:=\: 158\: cm }$

$\mathtt{⇢\: Average\: height \: when\: 1 \:girl\: is\: neglected \:= \:159\: cm }$

${\underline{\mathtt{\green{To\: Find⇢}}}}$

$\mathtt{⇢\: Height\: of \:neglected \:girl}$

________________________

${\boxed{\mathtt{\green{Formula \:of \:average\:⇢}}}}$

$⇢ \: \frac{sum \: of \: total \: observations}{number \: of \: observations}$

$\mathtt{⇢\:Let\: us \:assume\: that\: sum\: of\: height }$

$\mathtt{ of\: 10\:girls\: is \:<strong>x</strong><strong> </strong> }$

$⇢ \: \frac{x}{10} = 158$

$⇢ \: x = 1580$

$\mathtt{⇢\: Now \: assume\: that\: the \:height\: of \:neglected\: girl\: is\: <strong>y</strong>}$

$\mathtt{⇢\:Sum \:of \:height \:of \:9 \:girls\:=\: x \:- \:y}$

$⇢ \: \frac{x - y}{9} = 159$

$⇢ \: x - y = 1431$

$⇢ \: y = x - 1431$

$\mathtt{⇢\:Here \:we \:will\: put \:the \:value\: of \:x }$

$⇢ \: y = 1580 - 1431$

${ \boxed{\mathtt{ \purple{⇢ \: y = 149}}}}$

${\boxed{\mathtt{\green{⇢\: So\: the \:height \:of\: neglected\: girl\: is\: 149 \:cm}}}}$