Question

16. Using short cut method, compute the mean height from the following frequency distribut
Height (in cm) 58 60 62 65 66 68
Number of plants
15 14 20 18.
8
5
​

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 = $\sf l + \bigg( \dfrac{ f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h$