If the median of the distribution …

Here, {tex}\sum f _ { i } = n = 60{/tex}, then {tex}\frac { n } { 2 } = \frac { 60 } { 2 } = 30{/tex}, also, median of the distribution is 28.5, which lies in interval 20 – 30.

{tex}\therefore{/tex} Median class = 20 – 30

So, l = 20, n = 60, f = 20, cf = 5 + x and h = 10

{tex}\because 45 + x + y = 60{/tex}

{tex}\Rightarrow x + y = 15{/tex} ………...........(i)

Now, Median = {tex}l + \left[ \frac { \frac { n } { 2 } - c f } { f } \right] \times h{/tex}

{tex}\Rightarrow { 28.5 = 20 + \left[ \frac { 30 - ( 5 + x ) } { 20 } \right] \times 10 }{/tex}

{tex}\Rightarrow 28.5 = 20 + \frac { 30 - 5 - x } { 2 }{/tex}

{tex}\Rightarrow { 28.5 } = \frac { 40 + 25 - x } { 2 }{/tex}

{tex}\Rightarrow 2 ( 28.5 ) = 65 - x{/tex}

{tex}\Rightarrow 57.0 = 65 - x{/tex}

{tex}\Rightarrow x = 65 - 57 = 8{/tex}

{tex}\Rightarrow{/tex} x = 8

Putting the value of x in eq. (i), we get,

8 + y = 15

{tex}\Rightarrow{/tex} y = 7

Hence the value of x and y are 8 and 7 respectively.