Question

Find the value of following data is 21.6, Find the value of p

Xi=6,12,18,24,30,36 and Fi=5,4,p,6.4,6

Answer 1

AnswEr :

$\begin{tabular}{| c | c | c | c | c | c | c |}\cline{1-7}</p><p>\bf{xi} & \sf{6} & \sf{12} & \sf{18} & \sf{24} & \sf{30} & \sf{36}\\ \cline{1-7}\bf{fi} & \sf{5} & \sf{4} & \sf{p} & \sf{6} & \sf{4} & \sf{6}\\ \cline{1-7} \end{tabular}$

$\rule{100}1$

$\begin{tabular}{| c | c | c | }\cline{1-3}</p><p>\bf{xi} & \bf{fi} & \bf{fixi}\\ \cline{1-3}\sf{6} & \sf{5} & \sf{30}\\ \cline{1-3}\sf{12} & \sf{4} & \sf{48}\\ \cline{1-3}\sf{18} & \sf{p} & \sf{18p}\\ \cline{1-3}\sf{24} & \sf{6} & \sf{144}\\ \cline{1-3}\sf{30} & \sf{4} & \sf{120}\\ \cline{1-3}\sf{36} & \sf{6} & \sf{216}\\ \cline{1-3}\sf{Total } & \sum\limits\sf\ fi \sf\ = 25 +p & \sum\limits\sf\ fixi \sf\ = 558 + 18p \\ \cline{1-3} \end{tabular}$

$\rule{200}2$

$\normalsize\star{\boxed{\sf{Mean \left( \bar{x} \right) = \frac{\sum\limits\ f_i x_i}{\sum\limits\ f_i} }}}$

$\normalsize\dashrightarrow\sf\ 21.6 = \frac{558 + 18p}{25 + p}$

$\scriptsize\sf{ \: \: \: \: \: \: \: \: \: \dag\ Cross \: multiplication}$

$\normalsize\dashrightarrow\sf\ 21.6(25 + p) = 558 + 18p$

$\normalsize\dashrightarrow\sf\ 540 + 21.6p = 558 + 18p$

$\normalsize\dashrightarrow\sf\ 558 - 540 = 21.6p - 18p$

$\normalsize\dashrightarrow\sf\ 18 = 3.6p$

$\normalsize\dashrightarrow\sf\ p = \frac{18}{3.6}$

$\normalsize\dashrightarrow\sf\ p = \frac{180}{36}$

$\normalsize\dashrightarrow\sf\ p = 5$

$\therefore\:\underline{\textsf{Hence, \: the \: value \: of \: p \: is}{\textbf{\: \: 5 }}}$

Answer 2

$\Huge\mathrm{Question: }$

⟶ Find the value of p when the mean of the Following data is 21.6 .

Xi = 6 , 12 , 18 , 24 , 30 , 36

Fi = 5 , 4 , p , 6 , 4 , 6

$\Huge\mathrm{Answer:}$

${\large{\boxed{\mathbb{\red{⟶ VALUE \: OF \: P = 5 }}}}}$

$\huge\mathrm{Explanation:}$

$\mathfrak\purple{Refer \: to \: the \: attachments! ♡♡}$

$\Large\mathbb{OR}$

⟹ $\sf\blue{Mean = 21.6}$

⟹ $\sf\red{Mean = \frac{ \sum fixi}{ \sum fi} }$

⟹ $\sf\green{=\frac{558+18p}{25+p} }$

⟹ $\mathbb\orange{THUS,}$

⟹ $\sf\purple{21.6 = \frac{558+18p}{25+p} }$

⟹ $\sf\blue{21.6 ( 25+p ) = 558 + 18p}$

⟹ $\sf\red{540+21.6p = 558+18p}$

⟹ $\sf\green{21.6p-18p = 558 -540}$

⟹ $\sf\orange{3.6p= 18}$

⟹ $\sf\purple{p = \cancel{18} \times \cancel{\frac{10}{36} } }$

⟹ $\large{\underline{\sf{Value \: of \: p = 5}}}$

$\huge\mathrm{ Verification : }$

$\sf{According \: To \: the \: Question :}$

$\sf{Mean = 21.6}$

$\sf{Value \: of \: p = 5}$

$\sf{ With \: reference \: to \: the \: tabulation :}$

$\sf{\sum Fixi= 558 + 18p = 558 + 18 \times 5 = 558 + 90 = 648}$

$\sf{\sum fi = 25 + p = 25 + 5 = 30 }$

$\sf{Mean = \frac{\sum fixi }{\sum fi} }$

$\sf{Mean = \frac{648 }{30} }$

$\sf{Mean = 21.6 }$

${\large{\boxed{\sf{21.6=21.6}}}}$

${\large{\boxed{\bf{Thus,\: verified! :)}}}}$