The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.
Class
(No. of mangoes) Frequency
(No. of trees) Cumulative frequency
(less than)
$50 - 100$ $33$ $33$
$100 - 150$ $30$ $63$
$150 - 200$ $90$ $153$
$200 - 250$ $80$ $233$
$250 - 300$ $17$ $250$

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Solution

Here, $n = 250$ then, $\frac{n}{2} = \frac{250}{2} = 125$
$\Rightarrow$ Median class $= 150 - 200$
$l = 150, c f = 63, f = 90, h = 50$
$\Rightarrow$ $M e d i a n = l + \frac{\frac{n}{2} - c f}{f} \times h$

$= 150 + \frac{125 - 63}{90} \times 50$

$= 150 + 34.44$
$= 184.44$

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Class (No. of mangoes)	Frequency (No. of trees)	Cumulative frequency (less than)
$50 - 100$	$33$	$33$
$100 - 150$	$30$	$63$
$150 - 200$	$90$	$153$
$200 - 250$	$80$	$233$
$250 - 300$	$17$	$250$

Here, n=250 then, n2=2502=125⇒ Median class =150−200l=150,cf=63,f=90,h=50⇒ Median=l+n2−cff×h =150+125−6390×50 =150+34.44 =184.44

Here, $n = 250$ then, $\frac{n}{2} = \frac{250}{2} = 125$
$\Rightarrow$ Median class $= 150 - 200$
$l = 150, c f = 63, f = 90, h = 50$
$\Rightarrow$ $M e d i a n = l + \frac{\frac{n}{2} - c f}{f} \times h$

$= 150 + \frac{125 - 63}{90} \times 50$

$= 150 + 34.44$
$= 184.44$