Question

Mean of 30 numbers is 18, what will be the new mean if each observation is increased by 2?​

Answer 1

$\bold\color{gold}{Obsevations\: is\: 30}$

$\bold\color{gold}{mean\: is \:18}$

$\small{So \:,mean\: the\: average\: if \:increased \:2\: times}$

As we know ,that observations be (x₁,x₂,x₃,x₃₀)

$\mathbb{Sum \:of \:observation}$

${ \large{ \boxed{ \red{ \underline{ \bf \:=(mean)(no\: of\: observation)}}}}}$

$\sf\color{blue}{=(18)(30)}$

$\sf\color{blue}{=540}$

So ,when each is increased by 2,then:

Sum of new observations:

$\sf{Σx₁=(x₁+2)+(x₂+2)+(x₃+2)+(x₄+2)+....(x₃₀+30)}$

$\bold{(x₁+x₂+x₃...+x₃₀)+2) x 30}$

$\sf{ =((18)+2) x 30}$

$\sf{ =540+60}$

$\huge\color{darkpink}{ =600}$

$\textbf{So,the average is:}$

$\bold{mean=Σx₁}$

no of new observations

$\sf\color{orange}{=600\30}$

$\sf\color{orange}{=20}$

Thankyou :)

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