Question

find the median of the following data marks and students 10-20=7,20-30=9,3040=10,40-50=12,50-60=5,60-70=7​

Answer 1

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$\text{\large\underline{\purple{Given:-}}}$

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Marks & \tt 10-20 & \tt 20-30 & \tt 30-40 & \tt 40-50 & \tt 50-60 & \tt 60-70\\\cline{1-7}\tt No. of Students &\tt 7 & \tt 9 & \tt 10 & \tt 12 & \tt 5 & \tt 7 \\\cline{1-7}\end{tabular}\end{gathered}$

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$\text{\large\underline{\green{To find:-}}}$

Median of the given data

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$\text{\large\underline{\red{Solution:-}}}$

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⋆ TABLE:

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$\begin{gathered}\boxed{\begin{array}{cccc}\sf Class\: interval&\sf Frequency&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 10 - 20&\sf 7&\sf 7\\\\\sf 20-30 &\sf 9&\sf 16 \\\\\sf 30-40 &\sf 10 &\sf 26\\\\\sf 40-50&\sf 12&\sf 38\\\\\sf 50-60 &\sf 5 &\sf 43 \\\\\sf 60-70 &\sf 7 &\sf 50\end{array}}\end{gathered}$

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Here,

Total no. of students, n = 50

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If N = 50

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$Then, \sf \dfrac{n}{2} = \cancel{ \dfrac{50}{2}}$

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As 26 is greater than 25, Therefore median class is 30-40.

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$\begin{gathered}\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here:\\1)\:l=Lower\:limit\:of\:median\:class=30\\2)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=16\\3)\:f= frequency\:of\:median\:class=10\\4)\:h= Class\:interval =40 - 30 = 10\end{minipage}}\end{gathered}$

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$\star\;{\boxed{\sf{\purple{ l + \dfrac{ \frac{n}{2} - C.f.}{f} \times h}}}}$

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

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$\implies\sf 30 + \dfrac{25 - 16}{10} \times\cancel{10}$

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$\implies\sf 30 + \dfrac{9}{ \cancel{10}} \times \cancel{10}$

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$\implies\sf {30 + 9}$

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$\implies{\underline{\boxed{\sf{\purple{39}}}}}$

${\underline{\boxed{\sf{\red{ ∴ Hence, \:Median \:of \:the \:given \:data\: is \:39.}}}}}$

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Answer 2

Answer:

Marks (x)  No. of students (f)  C.F.

0-10 15 15

10-20 20 35

20-30 25 60

30-40 24 84

40-50 12 96

50-60 31 127

60-70 71 198

70-80 52 250

 N = 250  

As, N=250⇒  

N  =250/2

N=125

As 127 is just greater than 125, therefore median class is 50−60.

Median=l+ f 2 N +C ×h

Here, l=lower limit of median class =50

C=C.F. of the class preceding the median class =96

h= higher limit - lower limit =60−50=10

f= frequency of median class =31

∴median=50+31

125−96×10=50+9.35=59.35

hope it helps you