Question

find missing frequency ???​

Answer 1

${\boxed{\bf{Frequency \: distribution \: table}}}$

$\bf{\underline{\orange{Class\:interval \qquad \qquad \qquad Frequency}}}$

$\bf{\underline{\quad 0 -10 \qquad \qquad \qquad \quad \qquad \qquad \quad 10\quad}}$

$\bf{\underline{\quad 10 -20 \qquad \qquad \qquad \quad \qquad \qquad \quad f_1\quad}}$

$\bf{\underline{\quad 20 -30 \qquad \qquad \qquad \quad \qquad \qquad \quad 25\quad}}$

$\bf{\underline{\quad 30 -40 \qquad \qquad \qquad \quad \qquad \qquad \quad 30\quad}}$

$\bf{\underline{\quad 40 -50 \qquad \qquad \qquad \quad \qquad \qquad \quad f_2\quad}}$

$\bf{\underline{\quad 50-60 \qquad \qquad \qquad \quad \qquad \qquad \quad 10\quad}}$

To find:-

Missing frequencies

Solution :-

$\large{\red{\underline{\boxed{\bf{\red{Median=\Bigg\left(l + \dfrac{\dfrac{N}{2} - cf}{f}\Bigg\right)\times{h}}}}}}}$

$\sf{l = Lower\:limit}$

$\sf{h =Width\:of\:class}$

$\sf{f = Frequency}$

$\sf{cf = Cumulative\:frequency (preceding\;class)}$

$\sf{M_e=Median}$

$\tt{\underline{\purple{According\:to\:given\: condition}}}$

$\tt{\blue{Let\;the\;missing\;frequencies\;be\;f_1\;and\;f_2}}$

$\sf{10-20(class\:interval)=f_1}$

$\sf{40-50(class\:interval=f_2}$

$\sf{Total\: frequency (N)=100}$

$\implies\tt{10+f_1+25+30+f_2+10=100}$

$\implies\tt{75+f_1+f_2=100}$

$\implies\tt{f_1+f_2=100-75}$

$\implies\tt{f_1+f_2=25}$

$\sf{l = 30}$

$\sf{h =10}$

$\sf{f = 30}$

$\sf{cf = (10+f_1+25)=f_1+35}$

$\sf{M_e=32}$

$\implies\tt{32=30 +\Bigg\left( \dfrac{ \dfrac{100}{2} - (f_1+35)}{30}\Bigg\right)\times{10}}$

$\implies\tt{32-30=\Bigg\left( \dfrac{50 - (f_1+35)}{30}\Bigg\right)\times{10}}$

$\implies\tt{2=\Bigg\left( \dfrac{50 - f_1 - 35}{30}\Bigg\right)\times{10}}$

$\implies\tt{2=\Bigg\left( \dfrac{50 - 35 - f_1}{30}\times{10}\Bigg\right)}$

$\implies\tt{2=\Bigg\left( \dfrac{15 - f_1}{3}\Bigg\right)}$

$\implies\tt{2\times{3}}=15 - f_1$

$\implies\tt{6=15-f_1}$

$\implies\tt{15-6=f_1}$

$\implies\tt{f_1=9}$

$\tt\underline{\purple{Now\:put\:the\:value\:of\:f_1}}$

$\implies\tt{f_1+f_2=25}$

$\implies\tt{9+f_2=25}$

$\implies\tt{f_2=25-9}$

$\implies\tt{f_2=16}$

$\underline{\tt{\purple{Hence,missing\: frequencies}}}$

$\tt{\qquad \qquad \qquad f_1=9}$

$\tt{\qquad \qquad \qquad f_2=16}$

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•• note :- ⭐ kindly see the answer from website otherwise u won't able to understand ⭐