Question

The mean of 5 number is 21 if one of the number is excluded then the mean of remaining numbers is is 22.5 the excluded number is

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Question :

The mean of 5 number is 21 if one of the number is excluded then the mean of remaining numbers is is 22.5 the excluded number is?

Given :

• Mean of 5 numbers = 21
• If one number is excluded then mean = 22.5

To find :

• Excluded number

Solution :

Mean of 5 numbers = 21

We know,

$: \implies\underline{\boxed{\sf{Mean = \dfrac{Sum \ of\ numbers}{Total \ number} }}} \\\\ \\ : \implies\sf 21 = \dfrac{Sum \ of \ 5 \ numbers}{5} \\\\ \\ : \implies\sf Sum \ of \ 5\ numbers = 21 \times 5 \\\\ \\ : \implies\bold{Sum \ of \ 5 \ numbers = 105} \dots\dots \ (i)$

Now mean of 4 numbers = 22.5

$: \implies\sf 22.5 = \dfrac{Sum \ of \ 4 \ numbers}{4} \\\\ \\ : \implies\sf Sum \ of \ 4 \ numbers = 4 \times 22.5 \\\\ \\ : \implies\bold{Sum \ of \ 4 \ numbers = 90} \dots\dots \ (ii)$

Now excluded number :

$: \implies\sf Excluded \ number = Sum \ of \ 5 \ numbers - Sum \ of \ 4 \ numbers \\\\ \\ : \implies\sf Excluded \ number = 105 - 90 \\\\ \\ : \implies\underline{\boxed{\sf{Excluded \ number = 15 }}} \ \star$

$\therefore\underline{\boxed{\textsf{Excluded number is = {\textbf{15}}}}} \qquad\qquad \bigg\lgroup\bold{Required \ answer} \bigg\rgroup$