Find the median of the following data : .
20-30 5
30-40 15
40-50 25
50-60 20
60-70 7
70-80 8
80-90 10
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Answers
AnswEr:−
\begin{gathered}\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 20 - 30&\sf 5&\sf 5\\\\\sf 30 - 40 &\sf 15&\sf 20\\\\\sf 40 - 50&\sf 25&\sf 45\\\\\sf 50 - 60&\sf 20&\sf 65\\\\\sf 60 - 70&\sf 7&\sf 72\\\\\sf 70 - 80&\sf 8&\sf 80\\\\\sf 80 - 90&\sf 10&\sf 90\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf & \bf \sum f = 90& \end{array}}\end{gathered}
Classinterval
20−30
30−40
40−50
50−60
60−70
70−80
80−90
Frequency(f)
5
15
25
20
7
8
10
∑f=90
C.F
5
20
45
65
72
80
90
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We know that,
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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)\:N = \sum \:f= 90\\2)\:l=Lower\:limit\:of\:median\:class=40\\3)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=20\\4)\:f= frequency\:of\:median\:class=25\\5)\:h= Class\:interval =40-30=10\end{minipage}}\end{gathered}
⠀━━━━━━━━━━━━━━━━━━━━━━━━
\begin{gathered}\underline{\bigstar\:\boldsymbol{According\; to \;the \;Question :}} \\ \\\end{gathered}
★AccordingtotheQuestion:
\begin{gathered}\dashrightarrow\sf\:\:\purple{Median = l +\dfrac{\frac{n}{2}-C.f.}{f}\times h}\\\\\\\dashrightarrow\sf\:\:Median = 40 +\bigg\lgroup\dfrac{45-20}{25}\times10\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 40 +\bigg\lgroup \cancel{\dfrac{25}{25}}\times10\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 40 +10\\\\\\\dashrightarrow\:\:\underline{\boxed{\pink{\sf Median = 50}}}\;\bigstar\end{gathered}
⇢Median=l+
f
2
n
−C.f.
×h
⇢Median=40+
⎩
⎪
⎪
⎪
⎧
25
45−20
×10
⎭
⎪
⎪
⎪
⎫
⇢Median=40+
⎩
⎪
⎪
⎪
⎧
25
25
×10
⎭
⎪
⎪
⎪
⎫
⇢Median=40+10
⇢
Median=50
★
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\therefore\:\underline{\textsf{Median of given data is \textbf{50}}}.∴
Median of given data is 50
.
I hope that help you