Find the median of the following observations.
Class interval:0-20 20-40 40-60 60-80 80-100 100-120.
Frequency:10 35 52 61 38 29.
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Find the median of the following observations.
Class interval:0-20 20-40 40-60 60-80 80-100 100-120.
Frequency:10 35 52 61 38 29.
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Find the mean, median and mode of the following data:
Class
0 – 20
20 – 40
40 – 60
60 – 80
80 – 100
100 – 120
120 – 140
Frequency
6
8
10
12
6
5
3
EXPLANATION: hope it's helpful for you PLEASE MARK ME AS BRAINLIST PLEASE PLEASE..........
Verified answer
[tex]\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Class & \tt 0-20 & \tt 20-40 & \tt 40-60 & \tt 60-80 & \tt 80-100 & \tt 100-120 \\\cline{1-7}\tt Frequency &\tt 10 & \tt 35 & \tt 52 & \tt 61 & \tt 38 & \tt 29 \\\cline{1-7}\end{tabular}\end{gathered}[/tex]
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We have to find, Median of given data.
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[tex]\boxed{\begin{array}{cccc}\bf Class\: interval&\bf Frequency\: (f) &\bf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0-20 &\sf 10 &\sf 10\\\\\sf 20-40 &\sf 35&\sf 45\\\\\sf 40-60 &\sf 52&\bf 97\\\\\bf 60-80&\bf 61&\sf 158\\\\\sf 80-100&\sf 38&\sf 196\\\\\sf 100-120& \sf 29 & \sf 225 \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf & \bf \sum f = 225& \end{array}}[/tex]
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[tex]\dag\;{\underline{\frak{Formula\;to\:find\;Median,}}}[/tex]
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[tex]\star\;{\boxed{\sf{\pink{l = \dfrac{ \frac{n}{2} - C.F.}{f} \times h}}}}[/tex]
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Firstly we have to calculate [tex]\sf \dfrac{n}{2}[/tex], (where N = [tex]\sf \sum F[/tex]) = [tex]\sf \dfrac{225}{2} = \bf{112.5}.[/tex]
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So, The value of comulative frequency just greater than or equal to 112.5 is 158.
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[tex]\dag\;{\underline{\frak{We\;know\;that,}}}[/tex]
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[tex]\boxed{\begin{minipage}{6cm}$\bigstar$\:\:\sf Median = l + $\sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here: \\1)\:n = \sum f =225\\2)\:l=Lower\:limit\:of\:median\:class=60\\3)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=97\\4)\:f= frequency\:of\:median\:class=61\\5)\:h= Class\:interval =80-60 = 20\end{minipage}}[/tex]
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[tex]{\underline{\sf{\bigstar\;Putting\;values\;in\;formula\;:}}}[/tex]
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[tex]:\implies\sf 60 + \dfrac{ \frac{225}{2} - 97}{61} \times 20[/tex]
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[tex]:\implies\sf 60 + \dfrac{112.5 - 97}{61} \times 20[/tex]
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[tex]:\implies\sf 60 + \dfrac{15.5}{61} \times 20[/tex]
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[tex]:\implies\sf 60 + 0.254 \times 20[/tex]
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[tex]:\implies\sf 60 + 5.08[/tex]
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[tex]:\implies{\underline{\boxed{\frak{\purple{65.08(approx.)}}}}}\;\bigstar[/tex]
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[tex]\therefore\;{\underline{\sf{Median\;of\;given\; distribution\;is\; \textbf{65.08}.}}}[/tex]