Question

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

Find the median of this frequency table.

✧ Don't give irrelevant answer.
✧ Spam answer = Deleted

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Answer 1

✯ Topic ☛ Data Handling .

✯ Your Question ☟

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

• Find the median of this frequency table.

✯ Methods For Finding The Median ☟

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.

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

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

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

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

✯ 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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✰ Hope it helps u ✰

Answer 2

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

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

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

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