Math, asked by IamSameerhii, 2 months ago

The shoe size of 30 players selected for interschool competitions are given attachment :

Find the median of this frequency table.

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Answers

Answered by TheBrainlyStar00001
130

TopicData Handling .

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Your Question

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  • The shoe size of 30 players selected for interschool competitions are given attachment :

  • Find the median of this frequency table.

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Methods For Finding The Median

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First arrange the terms in ascending or descending order. Now, prepare a comulative frequency table.

Let the total frequency be \sum \boldsymbol{f_{i}} be N.

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 \color{blue} \bf {Case \: 1.} \:  \:  \:  \tt \color{orange}  \underline{\: When \: N \: is \: odd, \: then : } \\

 \:  \:  \:  \:  \:  \:   \qquad:\implies   \tt\color{darkviolet}\: Median \:    :\implies \:   \bigg\lgroup \frac{N + 1}{2} \bigg\rgroup {}^{th} \: \:  item :   \\

 \color{blue} \bf {Case \: 2.} \:  \:  \:  \tt \color{orange}  \underline{\: When \: N \: is \: even, \: then : } \\

 \:  \:  \:  \:  \:  \:   \qquad:\implies   \tt\color{darkviolet}\: Median \:    :\implies \:    \frac{1}{2}. \bigg \lbrace \big\lgroup \frac{N}{2} \big\rgroup{}^{th}\: \:  item  +\big\lgroup\frac{N}{2} + 1\big\rgroup {}^{th} \:  \:  item \bigg  \rbrace     \\

Solution

 \\  ❍  \: \color{orange} \tt \underline{Arranging \: the \: terms \: in \: ascending \: order, \: we \: get : } \\  \\

In the Attachment .

 \\ ❍  \:  \tt  \color{orange}\underline{Now, \: we \:  prepare \: the \: comulative \: frequency \: table \:  : } \\  \\

In the Attachment .

 \\ ✧ \:  \:  \color{darkviolet} \tt  \underline{Total \: no. \: of \: terms \:   : {\small{ \implies}} \:  \sum \boldsymbol{ f_{i}}{\small{ \implies}}N{\small{ \implies}}30, \: which \: is \: even.} \\  \\

✰   \:  \: \bf  \underline{Finding \: Median \:  : } \\

 :\implies   \tt\color{darkviolet}\: Median \:    :\implies \:    \frac{1}{2}. \bigg \lbrace \big\lgroup \frac{N}{2} \big\rgroup{}^{th}\: \:  term  +\big\lgroup\frac{N}{2} + 1\big\rgroup {}^{th} \:  \:  term \bigg  \rbrace     \\ \:  \:  \:  \:  \:  :\implies   \tt\color{orange}\: Median \:    :\implies \:    \frac{1}{2}. \bigg \lbrace \big\lgroup \frac{30}{2} \big\rgroup{}^{th}\: \:  term +\big\lgroup\frac{30}{2} + 1\big\rgroup {}^{th} \:  \:  term \bigg  \rbrace     \\ :\implies   \tt\color{blue}\: Median \:    :\implies \: \frac{1}{2} (15 {}^{th}  \:  term+ 16 {}^{th}   \:  term) \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\ :\implies   \tt\color{skyblue}\: Median \:    :\implies \: \frac{1}{2} (8+ 9) \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:  \:  \:  \:  \:  \:  \:   \: :  \:  \:  \:  \: \:  \:  \:   \\ :\implies   \tt\color{green}\: Median \:    :\implies \:  \frac{17}{2}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:  \:  \:  \:  \:  \:  \:   \: :  \:  \:  \:  \: \:  \:  \:   \qquad \:  \:  \\      : \implies\underline{\boxed{  \bf \:{\colorbox{black}{\color{yellow} M}} \:  ➠ \:  \: \color{purple}{\frak{8.5}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad \\  \\

[ Note : Each one of 13th, 14th and 15th term is 8 and each one of 16th, 17th, \cdots, 23rd term is 9.]

 \\  \boldsymbol {\underline{ ✿\:\:Hence},} \:  \:  \underline {\tt{median \: {\small{  :  \implies}} \bf 8.5}}.

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Another Question Related to it :-

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https://brainly.in/question/37572040?utm_source=android&utm_medium=share&utm_campaign=question

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Hope it helps u

Attachments:
Answered by THEmultipleTHANKER
27

\begin{gathered} \\ ✧ \: \: \color{darkviolet} \tt \underline{Total \: no. \: of \: terms \: : {\small{ \implies}} \: \sum \boldsymbol{ f_{i}}{\small{ \implies}}N{\small{ \implies}}30, \: which \: is \: even.} \\ \\ \end{gathered}

\begin{gathered}✰ \: \: \bf \underline{Finding \: Median \: : } \\ \end{gathered}

\begin{gathered} :\implies \tt\color{darkviolet}\: Median \: :\implies \: \frac{1}{2}. \bigg \lbrace \big\lgroup \frac{N}{2} \big\rgroup{}^{th}\: \: term +\big\lgroup\frac{N}{2} + 1\big\rgroup {}^{th} \: \: term \bigg \rbrace \\ \: \: \: \: \: :\implies \tt\color{orange}\: Median \: :\implies \: \frac{1}{2}. \bigg \lbrace \big\lgroup \frac{30}{2} \big\rgroup{}^{th}\: \: term +\big\lgroup\frac{30}{2} + 1\big\rgroup {}^{th} \: \: term \bigg \rbrace \\ :\implies \tt\color{blue}\: Median \: :\implies \: \frac{1}{2} (15 {}^{th} \: term+ 16 {}^{th} \: term) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ :\implies \tt\color{skyblue}\: Median \: :\implies \: \frac{1}{2} (8+ 9) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: : \: \: \: \: \: \: \: \\ :\implies \tt\color{green}\: Median \: :\implies \: \frac{17}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: : \: \: \: \: \: \: \: \qquad \: \: \\ : \implies\underline{\boxed{ \bf \:{\colorbox{black}{\color{yellow} M}} \: ➠ \: \: \color{purple}{\frak{8.5}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad \\ \\ \end{gathered}

\begin{gathered} \\ \boldsymbol {\underline{ ✿\:\:Hence},} \: \: \underline {\tt{median \: {\small{ : \implies}} \bf 8.5}}.\end{gathered}

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