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  4. Median of the following freq. dist. xi 3 6 10 12 7 15 fi 3 4 2 8 13 10

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Q. Median of the following freq. dist.
$x_i$ 3 6 10 12 7 15
$f_i$ 3 4 2 8 13 10

Statistics

Solution:

We arranged the value of variate $x_i$ in ascending order with their frequencies
$x_i$ 3 6 10 12 7 15
$f_i$ 3 4 2 8 13 10

Here $N=40$ (even)
$\therefore \text { Median } =\frac{\left(\frac{ N }{2}\right) \text { th term }+\left(\frac{ N }{2}+1\right) \text { th term }}{2}$
$ =\frac{(20) \text { th term }+(21) \text { th term }}{2} $
$ =\frac{7+10}{2}=8.5$