Question

Draw 'less than ogive' and 'more than ogive' for the
following distribution and hence find its median

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Answer 1

$\large\underline{\sf{Solution-}}$

Given data is

$\:\begin{gathered} \begin{array}{|c|c|} \bf{Class  \: Interval} & \bf{Number \: of \: students} \\ 20 - 30 & 25  \\30 - 40 & 15 \\40 - 50 & 10 \\50 - 60 & 6 \\60 - 70 & 24\\70 - 80 & 12\\80 - 90 & 8 \end{array}\end{gathered}$

Frequency distribution table for Less than Ogive

$\: \: \begin{gathered} \begin{array}{|c|c|} \bf{Less  \: than} & \bf{Cumulative \: Frequency} \\ 30 & 25  \\40 & 40 \\50 & 50 \\60 & 56 \\70 & 80\\80 & 92\\90 & 100 \end{array}\end{gathered}$

Frequency distribution table for More than Ogive

$\:  \: \begin{gathered} \begin{array}{|c|c|} \bf{More  \: than} & \bf{Cumulative \: Frequency} \\ 20  & 100  \\30 & 75 \\40 & 60 \\50  & 50 \\60 & 44\\70  & 20\\80  & 8 \end{array}\end{gathered}$

We know,

The x - coordinate of point of intersection of Less than ogive and More than ogive gives median.

So,

From graph, we conclude that Median = 50