Question

The mean of 8 observations is 50 if 5 is added to each observation then find then find the vaule new mean

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\: Given:-\:\:\:}}$

Mean of 8 observation is 50

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

Each observation is increased by 5

So we have to find the value of mean

• Now

$\boxed{\sf{Mean= \dfrac{sum\:of\: observation}{No\:of\: observation}}}$

$\sf\underline{\pink{\:\:\:\: Solution:-\:\:\:\:}}$

• Let the numbers be x1,x2 ........x8

$\sf\implies 50=\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8}{8}\\ \\ \sf\implies 50\times 8=x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8\\ \\ \sf\implies 400= x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8\\ \\ \sf\bullet each\: observation\:is\: increased\:by\:5\\ \\ \sf\implies x_1+5+x_2+5+x_3+5+x_4+5+x_5+5+x_6+5+x_7+5+x_8+5\\ \\ \sf\implies 40+(x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8)\\ \\ \sf\implies 400=x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8\\ \\ \sf\implies 400+40 =440\\ \\ \sf\implies \bullet Now \:new \:mean\\ \\ \sf \bullet \:\:\:sum\:of\: observation 440\\ \\ \sf\:\:\:No.\:of\: observation=8\\ \\ \sf\implies mean=\dfrac{440}{8}\\ \\ \sf\implies mean=55$

$\boxed{\sf{\:\:mean\:of\:new\: observation=55}}$