Question

The following distribution shows the daily pocket money of children of a
school :
Daily Pocket Money (Rs.) 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Number of Children 7 6 9 13 20 5 4
Find the average daily pocket money of children.

Answer 1

AnswEr :

$\underline{\bigstar\:\textsf{As \: per \: given \: in \: question:}}$

$\begin{tabular}{| c | c | c | c | c | c | c | c |}\cline{1-8} </p><p>\bf{Daily \: pocket \: money } & \sf{11-13} & \sf{13-15} & \sf{15-17} & \sf{17-19} & \sf{19-21} & \sf{21-23} & \sf{23-25} \\ \cline{1-8}\bf{No. \: of \: children} & \sf{7} & \sf{6} & \sf{9} & \sf{13} & \sf{20} & \sf{5} & \sf{4} \\ \cline{1-8}\end{tabular}$

$\bullet$ We have to find Average daily income or Mean of the following data

$\underline{\bigstar\:\textsf{Let's \: head \: to \: the \: question \: now:}}$

$\begin{tabular}{| c | c | c | c |}\cline{1-4}</p><p>\bf{Class interval} & \bf{Frequency(fi)} & \bf{xi} & \bf{fixi}\\ \cline{1-4}\sf{11-13} & \sf{7} & \sf{12} & \sf{84}\\ \cline{1-4}\sf{13-15} & \sf{6} & \sf{14} & \sf{84}\\ \cline{1-4}\sf{15-17} & \sf{9} & \sf{16} & \sf{144}\\ \cline{1-4}\sf{17-19} & \sf{13} & \sf{18} & \sf{234}\\ \cline{1-4}\sf{19-21} & \sf{20} & \sf{20} & \sf{400}\\ \cline{1-4}\sf{21-23} & \sf{5} & \sf{22} & \sf{110}\\ \cline{1-4}\sf{23-25} & \sf{4} & \sf{24} & \sf{96}\\ \cline{1-4}\sf{Total =} & \sf{64} & \sf{} & \sf{1,152}\\ \cline{1-4}\end{tabular}$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{Make \: a \: table \: to \: represent \: values}) }$

$\rule{100}2$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{ Using \: direct \: method}) }$

$\large\ : \implies{\boxed{\sf \red{Mean = \frac{\sum\limits f_i x_i}{\sum\limits f_i}}}}$

$\normalsize\ : \implies\sf\ Mean = \frac{\cancel{1,152}}{\cancel{64}} \\ \\ \normalsize\ : \implies\sf\ Mean = 18$

$\therefore\underline{\textsf{Average \: daily \: pocket \: money \: of \: children \: is \: 18 \: rupees}}$

$\rule{100}2$

Other methods to find Mean :

$\star\normalsize{\boxed{\sf \green{Assumed_{method} = a + \frac{\sum\limits f_i d_i}{\sum\limits\ d_i} }}}$

$\star\normalsize{\boxed{\sf \blue{Step \: deviation_{method} = a + \frac{\sum\limits f_i u_i}{\sum\limits u_i} \times\ h }}}$