Question

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.​

Answer 1

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..........

Answer 2

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Class & \tt 0-20 & \tt 20-40 & \tt 40-60 & \tt 60-80 & \tt 80-100 & \tt 100-120 \\\cline{1-7}\tt Frequency &\tt 10 & \tt 35 & \tt 52 & \tt 61 & \tt 38 & \tt 29 \\\cline{1-7}\end{tabular}\end{gathered}$

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We have to find, Median of given data.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\begin{array}{cccc}\bf Class\: interval&\bf Frequency\: (f) &\bf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0-20 &\sf 10 &\sf 10\\\\\sf 20-40 &\sf 35&\sf 45\\\\\sf 40-60 &\sf 52&\bf 97\\\\\bf 60-80&\bf 61&\sf 158\\\\\sf 80-100&\sf 38&\sf 196\\\\\sf 100-120& \sf 29 & \sf 225 \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf & \bf \sum f = 225& \end{array}}$

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$\dag\;{\underline{\frak{Formula\;to\:find\;Median,}}}$

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$\star\;{\boxed{\sf{\pink{l = \dfrac{ \frac{n}{2} - C.F.}{f} \times h}}}}$

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Firstly we have to calculate $\sf \dfrac{n}{2}$, (where N = $\sf \sum F$) = $\sf \dfrac{225}{2} = \bf{112.5}.$

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So, The value of comulative frequency just greater than or equal to 112.5 is 158.

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

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$\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here: \\1)\:n = \sum f =225\\2)\:l=Lower\:limit\:of\:median\:class=60\\3)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=97\\4)\:f= frequency\:of\:median\:class=61\\5)\:h= Class\:interval =80-60 = 20\end{minipage}}$

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${\underline{\sf{\bigstar\;Putting\;values\;in\;formula\;:}}}$

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$:\implies\sf 60 + \dfrac{ \frac{225}{2} - 97}{61} \times 20$

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$:\implies\sf 60 + \dfrac{112.5 - 97}{61} \times 20$

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$:\implies\sf 60 + \dfrac{15.5}{61} \times 20$

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$:\implies\sf 60 + 0.254 \times 20$

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$:\implies\sf 60 + 5.08$

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$:\implies{\underline{\boxed{\frak{\purple{65.08(approx.)}}}}}\;\bigstar$

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$\therefore\;{\underline{\sf{Median\;of\;given\; distribution\;is\; \textbf{65.08}.}}}$