Question

question from statistic

please solve it​

Answer 1

$\begin {tabular} {|c|c|c|c|}\\\cline{1-4} class&f_{i}&x_{i}&f_{i}x_{i} \\\cline{1-4} 0-20&12&10&120 \\\cline{1-4} 20-40&15&30&450\\\cline{1-4} 40-60&32&50&1600\\\cline{1-4} 60-80&x&70&70x\\\cline{1-4} 80-100&13&90&1170\\\cline{1-4} -&\sum f_{i} =72+x&- &\sum f_{i}x_{i} =3340+70x\\\cline{1-4} \end {tabular}$

$Given \: mean = 53$

$\implies \frac{ \sum f_{i}x_{i}}{\sum f_{i} } = 53$

$\implies \frac{3340+70x}{72+x} = 53$

$\implies 3340 + 70x = 53(72+x)$

$\implies 3340 + 70x = 3816 + 53x$

$\implies 70x - 53x = 3816 - 3340$

$\implies 17x = 476$

$\implies x = \frac{476}{17}$

$\implies x = 28$

Therefore.,

$\red{ Value \: of \: x } \green{ = 28 }$

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