Question

Find the median of the following data: 15,12,11,20,9,5,18,16,14,13,19​

Answer 1

$\underbrace{\large{\underline{\sf Understanding\: the\: concept :}}}$

To find median firstly we should arrange all the observation in ascending order then we should check the sequence and find middle term in that sequence of ascending order & If there are even number of observations there is no middle time right? So, We should check and find out the two middle observations and then divide it by 2.

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As we know that,

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$\sf {Data} \begin{cases} \sf{15,12,11,20,9,5,18,16,14,13,19 } \end {cases}$

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$\begin{gathered}\underline{\textbf{ \textsf{Finding \: median :}}} \\ \\ \\ \sf : \implies1,3,5,9,11,12,13,15,16,18,19 \\ \\ \\ \boxed{\bf : \implies 12}\end{gathered}$

Hence, The median of 15, 12 ,11 ,20 ,9 ,5 ,18 ,16 ,14 ,13 ,19 is 12.

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$\begin{gathered}\boxed {\begin{array}{cc}\\ \dag \: \underline{\Large\bf Formulas\:of\:Statistics} \\ \\ \bigstar \: \underline{\rm Mean:} \\ \\ \bullet\sf M=\dfrac {\Sigma x}{n} \\ \\ \bullet\sf M=a+\dfrac {\Sigma fy}{\Sigma f} \\ \\ \bullet\sf M=A +\dfrac {\Sigma fy^i}{\Sigma f}\times c \\ \\ \bigstar \: \underline{\rm Median :} \\ \\ \bullet\sf M_d=\dfrac {n+1}{2} \:\left[\because n\:is\:odd\:number\right] \\ \\ \bullet\sf M_d=\dfrac {1}{2}\left (\dfrac {n}{2}+\dfrac {n}{2}+1\right)\:\left[\because n\:is\:even\:number\right] \\ \\ \bullet\sf M_d=l+\dfrac {m-c}{f}\times i \\ \\ \bigstar \: {\boxed{\sf M_0=3M_d-2M}}\end {array}}\end{gathered}$