Question

The Mean Of Three Numbers Is 10. Two Of The Numbers Are 9 And 14. What Is The Third Number?

Please Give Correct Answer ​

Answer 1

Step-by-step explanation:

12= 9+14+3rd number/3

12×3=23+3rd number

36- 23 = 3rd number

13 is the third number

Answer 2

Given

• Mean of three numbers = 10
• Two of the numbers = 9 and 14

To find

• The third number

Solution

Let the third number be x.

Using formula :-

$\huge{\dag} \large \boxed {\underline{\bf \red{ mean = \dfrac{sum \: of \: observations}{no. \: of \: observations}}}}$

Substitute the values,

$\quad : \implies \sf \gray{10 = \dfrac{9 + 14 + x}{3} } \\ \\ \\ \quad : \implies \sf \gray{10 = \frac{23 + x}{3} } \\ \\ \\ \quad : \implies \sf \gray{10 \times 3 = 23 + x} \\ \\ \\ \quad : \implies \sf \gray{30 = 23 + x} \\ \\ \\ \quad : \implies \sf \gray{30 - 23 = x} \\ \\ \\ \quad : \implies \sf \gray{7 = x} \\ \\ \\ \bf \gray{the \: value \: of \: x = \pink7} \\ \\ \\ \therefore \bf \red{ \underline{the \: third \: number = 7 }}\bigstar$

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$\underbrace{\bf \purple{lets \: verify : }} \\ \\ \\\quad : \implies \sf \gray{10 = \frac{9 + 14 + x}{3} } \\ \\ \\ \tt{ substituting \: the \: value \: of \: x \: in \: rhs} \\ \\ \\ \quad : \implies \sf \gray{ \frac{9 + 14 + 7}{3} } \\ \\ \\ \quad : \implies \sf \gray{ \frac{30}{3} } \\ \\ \\ \quad : \implies \sf \gray{10} \\ \\ \\ \tt{lhs = rhs} \\ \\ \\ \dag \bf \orange{hence \: verified.}$

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Some related formulae :

$\boxed {\begin{minipage}{9.2 cm}\\  \dag \: \underline{\Large\bf Formulas\:of\:Statistics} \\ \\ \bigstar \: \underline{\rm Mean:} \\ \\ \bullet\sf M=\dfrac {\Sigma x}{n} \\ \bullet\sf M=a+\dfrac {\Sigma fy}{\Sigma f} \\ \\ \bullet\sf M=A +\dfrac {\Sigma fy^i}{\Sigma f}\times c \\ \\ \bigstar \: \underline{\rm Median :} \\ \\ \bullet\sf M_d=\dfrac {n+1}{2} \:\left[\because n\:is\:odd\:number\right] \\ \bullet\sf M_d=\dfrac {1}{2}\left (\dfrac {n}{2}+\dfrac {n}{2}+1\right)\:\left[\because n\:is\:even\:number\right] \\ \\ \bullet\sf M_d=l+\dfrac {m-c}{f}\times i \\ \\ \bigstar \: {\boxed{\sf M_0=3M_d-2M}}\end {minipage}}$