Question

the mean of 5 number is 30 . if one number is excluded their mean becomes 28 what is excluded number.​

Answer 1

$\large\sf\underline{Given\::}$

• Mean of five numbers = 30

• When one number is excluded mean becomes 28

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$\large\sf\underline{To\:find\::}$

• The number which was excluded

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$\large\sf\underline{Solution\::}$

Let the five numbers be :

• a , b , c , d and e

We know ,

$\small{\underline{\boxed{\mathrm\pink{※\:Mean\:=\:\frac{Sum\:of\:observations}{Total\:number\:of\:observations}}}}}$

• Substituting the values

$\sf\:Mean\:=\frac{a+b+c+d+e}{5}$

$\sf\implies\:30\:=\frac{a+b+c+d+e}{5}$

• Cross multiplying

$\sf\implies\:a+b+c+d+e=5 \times 30$

$\sf\implies\:a+b+c+d+e=150---(i)$

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Now let the number excluded be a.

Assuming so we get :

$\sf\:Mean\:=\:\frac{b+c+d+e}{4}$

• Substituting the given value of mean

$\sf\implies\:28\:=\:\frac{b+c+d+e}{4}$

• Cross multiplying

$\sf\implies\:b+c+d+e=4 \times 28$

$\sf\implies\:b+c+d+e=112---(ii)$

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Substituting the value of ( b+c+d+e ) from (ii) in (i)

$\sf\implies\:a+b+c+d+e=150$

$\sf\implies\:a+112=150$

• Transposing 112 to the other side

$\sf\implies\:a=150-112$

$\large{\mathfrak\red{\implies\:a\:=\:38}}$

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$\dag\:\underline{\sf So\:the\:required\:excluded\:number\:is\:38.}$

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!! Hope it helps !!

Answer 2

Answer:

Excluded number will be 48

Explanation:

Hope it help you