If median of the following frequency distribution is 35 then find the value of x.
Class interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 2 3 x 6 5 3 2

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Solution

Class interval frequency cumulitative frequency
$0 - 10$ $2$ $2$
$10 - 20$ $3$ $5$
$20 - 30$
$x$ $5 + x$
$30 - 40$ $6$ $11 + x$
$40 - 50$ $5$ $16 + x$
$50 - 60$ $3$ $19 + x$
$60 - 70$ $2$ $21 + x$
Total frequency= $21 + x$
=> N= $21 + x$
=> $\frac{N}{2} = \frac{21 + x}{2}$
So; CF corresponding to this is $11 + x$
And class corresponds to this is $30 - 40$
So, $l = 30$ , $F = 5 + x$ , $f = 6$ and $h = 10$
$M e d i a n = l + ⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{N}{2} - F}{f} ⎞ ⎟ ⎟ ⎟ ⎠ \times h$
=> $35 = 30 + ⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{21 + x}{2} - 5 - x}{6} ⎞ ⎟ ⎟ ⎟ ⎠ \times 10$
=> $x = 5$

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100

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