Question

# The following table gives the heights (in metres) of 360 trees: Height Number of trees Less than 7 m Less than 14 m Less than 21 m Less than 28 m Less than 35 m Less than 42 m Less than 49 m Less than 56 m 25 45 95 140 235 275 320 360 From the above data, draw an ogive and find the median.

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Solution

## $\mathrm{We}\mathrm{plot}\mathrm{the}\mathrm{points}\mathrm{A\left(7,25\right),}\mathrm{B\left(14,45\right),}\mathrm{C\left(21,95\right),}\mathrm{D\left(28,140\right),}\mathrm{E\left(35,235\right)},\mathrm{F\left(42,275\right),}\mathrm{G\left(49,320\right)}\mathrm{and}\mathrm{H\left(56,360\right) .}\phantom{\rule{0ex}{0ex}}\mathrm{Join}\mathrm{AB,}\mathrm{BC,}\mathrm{CD,}\mathrm{DE,}\mathrm{EF,}\mathrm{FG,}\mathrm{GH}\mathrm{and}\mathrm{HA}\mathrm{with}a\mathrm{free}\mathrm{hand}\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{curve}\mathrm{representing}\mathrm{the}\text{'}\mathrm{less}\mathrm{than}\mathrm{type}\text{'}\mathrm{series}.$ $\mathrm{Here,}\mathrm{N=360}\phantom{\rule{0ex}{0ex}}⇒\mathrm{N/}2=180\phantom{\rule{0ex}{0ex}}\mathrm{From}\mathrm{P\left(0,180\right)},\mathrm{draw}\mathrm{PQ \parallel x}-\mathrm{axis}\mathrm{meeting}\mathrm{the}\mathrm{curve}\mathrm{at}\mathrm{Q.}\phantom{\rule{0ex}{0ex}}\mathrm{Draw}\mathrm{QM\perp OX}\mathrm{meeting}\mathrm{the}\mathrm{x-axis}\mathrm{at}\mathrm{M.}\phantom{\rule{0ex}{0ex}}\mathrm{Clearly},\mathrm{OM= 32.}5\mathrm{m}\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{median=32.}5\mathrm{m}$

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