Math, asked by karaibilBatmanBastiR, 5 months ago

38. The following distribution
gives the monthly
consumption of electricity of
68 thousands of a locality. Find
the median. 65-85 --4, 85-
105--5, 105-125--13, 125-145-
-20, 145-165--14, 165-185--8,
185-205--4.​

Answers

Answered by Madankumar808103
0

Answer:

38. The following distribution

gives the monthly

consumption of electricity of

68 thousands of a locality. Find

the median. 65-85 --4, 85-

105--5, 105-125--13, 125-145-

-20, 145-165--14, 165-185--8,

185-205--4.

hii

Answered by Salmonpanna2022
2

Step-by-step explanation:

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c} \qquad&\qquad&\qquad \\ \sf Class( Marks)&\sf Frequency(f)&\sf  ~ \sf Cumulative ~   \\ && \sf{frequency(cf)}\\ \hline \sf 65-85& \sf4& \sf4\\\hline \sf85-105&\sf5&\sf9 \\\hline \sf105-125&\sf 13&\sf 22 \\ \hline \sf125-145 &\sf 20&\sf 42\\\hline \sf145-165&\sf 14&\sf 56 \\\hline \sf165-185&\sf 7&\sf 63\\\hline \sf185-205&\sf 4&\sf 67\end{array}} \\ { \sf N = \sum}f   = 67\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}

\textsf{We know that,}\\

{\bf{Median = l+ \Bigg\{ h × \dfrac{\left(\dfrac{N}{2} - cf\right)}{f} }  \Bigg \}}

\textsf{Where}\\

\textsf{l = lower limit of median class,}

\textsf{n = number of observations,}

\textsf{cf = cumulative frequency of class preceding the median class, }

\textsf{f = frequency of median class,}

\textsf{h = class size (assuming class size to be equal).}

\textsf{l= 125 , (n) = 67 , (cf) = 22 , (f) = 20 (h) = 20}\\

\textsf{On substituting the values in Formula we get}\\

\sf{~~~~~:~~\implies Median = 125+ \Bigg\{ 20 × \dfrac{\left(\dfrac{67}{2} - 20\right)}{20} }  \Bigg \}

\sf{~~~~~:~~\implies Median = 125+ \Bigg\{  \xcancel{20} × \dfrac{33.5 - 22}{ \xcancel{20}} }  \Bigg \}

\sf{~~~~~:~~\implies Median = 125+ 11.5}

\sf{~~~~~:~~\implies Median = 136.5} \\  \\  \\

 \bf \underline{Hence, the\:median \:of \:electricity\: consumed \:is\: 136.5.}\\

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