Question

plzzz solve it.. .,.,.​

Answer 1

Question:-

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Using short cut method, compute the mean height from the following frequency distribution:

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$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt height& \tt 58 & \tt 60 & \tt 62 & \tt 65 & \tt 66 & \tt 68\\\cline{1-7}\tt no.of plant &\tt 15 & \tt 14& \tt 20&\tt 18 & \tt 8& \tt 5 \\\cline{1-7}\end{tabular}\end{gathered}$

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AnswEr:-

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$\boxed{\begin{array}{cccc}\bf Height \: (x_i)&\bf No. \: of \: plants \: (f_i)&\bf f_ix_i\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 58&\sf 15&\sf 870 \\\\\sf 60 &\sf 14&\sf 840\\\\\sf 62 &\sf 20 &\sf 1240\\\\\sf 65&\sf 18&\sf 1170\\\\\sf 66&\sf 8&\sf 528\\\\\sf 68 &\sf 5 &\sf 340 \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\bf &\bf \sum f_i = 80 &\bf \sum f_ix_i = 4988\end{array}}$

★ Now, Finding Mean Height,

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$\dag\;{\underline{\frak{We\;know\;that\;:}}}$

$\star\;{\boxed{\sf{\purple{ Mean\;(\bar{x}) = \dfrac{ f_i x_i}{f_i}}}}}$

$:\implies\sf \dfrac{4988}{80}$

$:\implies{\boxed{\sf{\pink{62.35}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Mean\; height\;of\;given\;data\;is\; {\textsf{\textbf{62.35}}}.}}}$

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$\qquad\quad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:Some\:formulas\:related\: to\:it\:\bigstar}}}}$

Formula to find Median of grouped frequency table = $\sf l + \bigg( \dfrac{\frac{N}{2} - C.F.}{f} \bigg) \times h$

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Formula to find Mode of grouped frequency table = $\sf l + \bigg( \dfrac{ f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h$

Answer 2

Answer:

Using short cut method, compute the mean height from the following frequency distribution:

$AnswEr:-</p><p></p><p>⠀⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered}\boxed{\begin{array}{cccc}\bf Height \: (x_i)&\bf No. \: of \: plants \: (f_i)&\bf f_ix_i\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 58&\sf 15&\sf 870 \\\\\sf 60 &\sf 14&\sf 840\\\\\sf 62 &\sf 20 &\sf 1240\\\\\sf 65&\sf 18&\sf 1170\\\\\sf 66&\sf 8&\sf 528\\\\\sf 68 &\sf 5 &\sf 340 \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\bf &\bf \sum f_i = 80 &\bf \sum f_ix_i = 4988\end{array}}\end{gathered}Height(xi)586062656668No.ofplants(fi)1514201885∑fi=80fixi87084012401170528340∑fixi=4988</p><p></p><p>★ Now, Finding Mean Height,</p><p></p><p>⠀⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered}\dag\;{\underline{\frak{We\;know\;that\;:}}}\\ \\\end{gathered}†Weknowthat:</p><p></p><p>\begin{gathered}\star\;{\boxed{\sf{\purple{ Mean\;(\bar{x}) = \dfrac{ f_i x_i}{f_i}}}}}\\ \\\end{gathered}⋆Mean(xˉ)=fifixi</p><p></p><p>\begin{gathered}:\implies\sf \dfrac{4988}{80}\\ \\\end{gathered}:⟹804988</p><p></p><p>\begin{gathered}:\implies{\boxed{\sf{\pink{62.35}}}}\;\bigstar\\ \\\end{gathered}:⟹62.35★</p><p></p><p>\therefore\;{\underline{\sf{Mean\; height\;of\;given\;data\;is\; {\textsf{\textbf{62.35}}}.}}}∴Meanheightofgivendatais62.35.</p><p></p><p>⠀━━━━━━━━━━━━━━</p><p></p><p>$