Question

If median of a given data is 63 then find the value of x.
29,32,48,50,x,x+2,72,78,84 and 90.

Answer 1

Median= (n/2)+(n/2+1)

=(10/2)+(10/2+1)

=x+x+2/2

63= x+(x+2)=x+1(x+2)/2

126= x+x+2

124=2x

x=62.

Answer 2

Observations are :-

29 ; 32 ; 48 ; 50 ;

x ; x+2 ;

72; 78 ; 84 ; 90

$\rule{200}{4}$

Now ,

Total number of observations = 10

So,

Since it is an even number then median will be as follows :-

$\boxed{ \sf{median = \dfrac{ \frac{n}{2} + (\frac{n}{2} + 1) }{2} {}^{th \: term}}}$

$\rule{200}{2}$

now,

We have :-

5th term = x

6th term = x+2

So,

Median (given) = 63

We have now :-

$\frac{x + x + 2}{2} = 63 \\ \\ \\ \frac{2(x + 1)}{2} = 63 \\ \\ \\x + 1 = 63 \\ \\ \\x = 63 - 1 = 62 \\ \\ \\ \boxed{x = 62}$

$\rule{200}{4}$

Hence,

$\boxed{\rm{x=62}}$