Question

Find the median of the given series.​

Answer 1

$\begin{tabular}{|c|c|c|}\cline{1-3} X & Frequency & C.f. \\\cline{1-3}0 - 10 & 3 & 3 \\\cline{1-3}10 - 20 & 7 & 10\\\cline{1-3}20 - 30 & 15 & 25\\\cline{1-3}30 - 40 & 9 & 34\\\cline{1-3}40 - 50 & 6 & 40\\\cline{1-3}50 - 60 & 4 & 44\\\cline{1-3}&\sum\limits N = 44&\\\cline{1-3}\end{tabular}$

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$\sf{Median\: class\: {\rightarrow\: Size\: of\: (\dfrac{N}{2})^{th} term}}$

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$\tt:\implies{Size\: of\: (\dfrac{44}{2})^{th} term}$

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$\tt:\implies{Size\: of\: (22)^{th} term}$

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$\therefore{Median\: class = (20 - 30)}$

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⌬ Formula of median is

$\large{\underline{\boxed{\tt{Median = L + \dfrac{\frac{N}{2} - C.f}{F} × i}}}}$

★ Where

• L = Lower limit
• C.f = Commutative frequency
• F = frequency
• i = class interval

⠀

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\begin{lgathered}\tt {\pink{Here}}\begin{cases} \sf{\green{L = 20}}\\ \sf{\blue{C.f = 10}}\\ \sf{\orange{F = 15}}\\ \sf{\purple{i = 10}}\end{cases}\end{lgathered} \:\end{lgathered}\end{lgathered}\end{lgathered}$

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★ Putting values in the formula

$\tt:\implies\: \: \: \: \: \: \: \: {M = 20 + \dfrac{22 - 10}{15} × 10}$

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$\tt:\implies\: \: \: \: \: \: \: \: {M = 20 + \dfrac{12}{15} × 10}$

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$\tt:\implies\: \: \: \: \: \: \: \: {M = 20 + 4 × 2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {M = 20 + 8}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{Median = 28\: units}}}}$

⠀

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