Question

if the sum of the deviations of a set of values x1 x2 x3 ...........xn measured from 50 is -10 and the sum of deviations of the values from 46 is 70 then find its mean​

Answer 1

Answer:

Please find the attachment

Answer 2

$\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}$

• If the sum of the deviations of a set of values $\bf{x_1\:,\:x_2\:,\:x_3\:........\:x_n\:}$ measured from 50 is -10 .

• And the sum of deviations of the values from 46 is 70 .

$\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}$

• The value of it's mean .

$\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}$

☯︎ According to the question,

ᴄᴀsᴇ - 1 ;-

✈︎ The sum of the deviations of a set of values $\bf{x_1\:,\:x_2\:,\:x_3\:........\:x_n\:}$ measured from 50 is -10 .

$\\ \bf{:\implies\:x_1\:-\:50\:+\:x_2\:-\:50\:+..........\:+\:x_n\:-\:50\:=\:-\:10\:}$

$\\ \bf{:\implies\:x_1\:+\:x_2\:+..........\:+\:x_n\:-\:50n\:=\:-\:10\:}$

$\\ \bf{:\implies\:x_1\:+\:x_2\:+..........\:+\:x_n\:=\:50n\:-\:10\:}----(1)$

ᴄᴀsᴇ - 2 ;-

✈︎ The sum of deviations of the values from 46 is 70 .

$\\ \bf{:\implies\:x_1\:-\:46\:+\:x_2\:-\:46\:+..........\:+\:x_n\:-\:46\:=\:70\:}$

$\\ \bf{:\implies\:x_1\:+\:x_2\:+..........\:+\:x_n\:-\:46n\:=\:70\:}$

$\\ \bf{:\implies\:x_1\:+\:x_2\:+..........\:+\:x_n\:=\:70\:+\:46n\:}----(2)$

☞︎︎︎ From equation (1) & (2), we get

$\\ \bf{:\implies\:50n\:-\:10\:=\:70\:+\:46n\:}$

$\\ \bf{:\implies\:50n\:-\:46n\:=\:70\:+\:10\:}$

$\\ \bf{:\implies\:4n\:=\:80\:}$

$\\ \bf{:\implies\:n\:=\:\dfrac{80}{4}\:}$

$\\ \bf\green{:\implies\:n\:=\:20\:}$

♪ We know that,

${\color{aqua}\bigstar}\:\bf{\pink{\overbrace{\underbrace{\blue{Mean\:=\:\dfrac{x_1\:+\:x_2\:+..........\:+\:x_n}{n}\:}}}}}$

☞︎︎︎ Putting the value of $\bf{x_1\:+\:x_2\:+........+\:x_n}$ in the above equation from equation (1), we get

$\\ \bf{:\implies\:Mean\:=\:\dfrac{50n\:-\:10}{20}\:}$

$\\ \bf{:\implies\:Mean\:=\:\dfrac{50\times{20}\:-\:10}{20}\:}$

$\\ \bf{:\implies\:Mean\:=\:\dfrac{1000\:-\:10}{20}\:}$

$\\ \bf{:\implies\:Mean\:=\:\dfrac{990}{20}\:}$

$\\ \bf\green{:\implies\:Mean\:=\:49.5\:}$

$\huge\purple\therefore$ The Mean is '49.5' .