Question

The mean of 6 numbers is 11. If five of them are 12, 10, 13, 7 and 8
then the 6th number is _____

Answer 1

Answer:

16

Step-by-step explanation:

$\huge \bf \underline{ \underline{☄ Question}}$

The mean of 6 numbers is 11. If five of them are 12, 10, 13, 7 and 8 then the 6th number is ___

$\huge \bf \underline{ \underline{☄ Answer}}$

$Mean = \frac{Sum\:of\:all\: the \: items \: of \: a \: series}{Total \: number \: of \: items}$

$Mean = 11$

$Total \: number \: of \: items \: = 6$

$Sum \: of \: the \: items \: =12+10+13+7+8+x$

$(Let \: the \: 6th \: number \: be \: x)$

$Putting \: the \: values \: in \: the \: formula: \\ \\11 = \frac{12 + 10 + 13 + 7 + 8 + x}{6} \\ \\ 11 = \frac{50 + x}{6}\\ \\ 11 \times 6 = 50 + x \\ \\66 = 50 + x \\ \\66 - 50 = x \\ \\ 16 = x$

Answer 2

$\sf\small\underline\purple{Given:-}$

$\tt{\implies Mean\:_{(6\:numbers)}= 11}$

$\tt{\implies 5\:numbers = 12,10,13,7,8}$

$\sf\small\underline\purple{To\:Find:-}$

$\tt{\implies 6th\:number}$

$\sf\small\underline\purple{Let:-}$

$\tt{\implies 6th\:number = x}$

$\sf\small\underline\purple{Formula\:used:-}$

$\tt{\implies Mean = \dfrac{Sum\:of\:observations}{Number\:of\:observations}}$

$\sf\small\underline\purple{We\:know\:that:-}$

$\tt{\implies Sum\:of\:observations = 12+10+13+7+8+x}$

$\tt{\implies Sum\:of\:observations = 50+x}$

$\tt{\implies Number\:of\:observations = 6}$

$\sf\small\underline\purple{Solution:-}$

$\tt{\implies Mean = \dfrac{Sum\:of\:observations}{Number\:of\:observations}}$

$\tt{\implies 11 = \dfrac{50+x}{6}}$

• On cross-multiplying, we get:

$\tt{\implies 11 \times 6 = 50+x}$

$\tt{\implies 66 = 50+x}$

$\tt{\implies 66-50 = x}$

$\tt{\implies 16 = x}$

$\tt{\implies x = 16}$

$\sf\small\underline\purple{Conclusion:-}$

$\tt{\implies 6th\:number = 16}$